Ad Sensing

Google has to approve your site before allowing you to join their partnership program. I don’t think they allow free hosting providers although you could try to submit your site in for review.
References :

I believe doing this is against the terms of service. I’m including the relevant section for review, but you’ll have to decide for yourself if you want to try this and find out.

7.2 Prohibited Uses

In addition to those matters set forth in the Yahoo! Policies, You shall not post, transmit, retransmit, or store material on or through any of the Services which, in the sole judgment of Yahoo! (i) is in violation of any local, state, federal, or foreign law or regulation, (ii) is threatening, obscene, indecent, defamatory, or that otherwise could adversely affect any individual, group, or entity (collectively, "Persons"), or (iii) violates the rights of any person, including rights protected by copyright, trade secret, patent, or other intellectual property or similar laws or regulations including, but not limited to, the installation or distribution of "pirated" or other software products that are not appropriately licensed for Your use. You agree that you will NOT knowingly use the Service, among other things, to:

(a) upload, post, email, transmit, or otherwise make available any content that is unlawful, harmful, threatening, abusive, harassing, tortious, defamatory, vulgar, obscene, libelous, invasive of another’s privacy, hateful, or racially, ethnically, or otherwise objectionable;

(b) harm minors in any way;

(c) impersonate any person or entity, including but not limited to a Yahoo! official, forum leader, guide, or host, or falsely state or otherwise misrepresent your affiliation with a person or entity;

(d) forge headers or otherwise manipulate identifiers in order to disguise the origin of any content transmitted through the Service;

(e) upload, post, email, transmit, or otherwise make available any content that You do not have a right to make available under any law or under contractual or fiduciary relationships (such as inside information, proprietary, and confidential information learned or disclosed as part of employment relationships or under nondisclosure agreements);

(f) upload, post, email, transmit, or otherwise make available any content that infringes any patent, trademark, trade secret, copyright, or other proprietary rights of any party;

(g) upload, post, email, transmit, or otherwise make available any unsolicited or unauthorized advertising, promotional materials, "junk mail," "spam," "chain letters," "pyramid schemes," or any other form of solicitation, except in those areas (such as shopping rooms) that are designated for such purpose;

(h) upload, post, email, transmit, or otherwise make available any material that contains software viruses or any other computer code, files, or programs designed to interrupt, destroy, or limit the functionality of any computer software or hardware or telecommunications equipment;

(i) interfere with or disrupt the Service or servers or networks connected to the Service, or disobey any requirements, procedures, policies, or regulations of networks connected to the Service;

(j) intentionally or unintentionally violate, attempt to violate, or avoid any applicable ICANN regulation or policy;

(k) intentionally or unintentionally violate any applicable local, state, national or international law, including, but not limited to, regulations promulgated by the U.S. Securities and Exchange Commission, any rules of any national or other securities exchange, including, without limitation, the New York Stock Exchange, the American Stock Exchange, or the NASDAQ, and any regulations having the force of law;

(l) provide material support or resources (or to conceal or disguise the nature, location, source, or ownership of material support or resources) to any organization(s) designated by the United States government as a foreign terrorist organization pursuant to section 219 of the Immigration and Nationality Act;

(m) "stalk" or otherwise harass another;

(n) collect, transmit, or store personal or financial data about any individual or entity, other than in accordance with Section 9.3 herein;

(o) promote or provide instructional information about illegal activities, promote physical harm or injury against any group or individual, or promote any act of cruelty to animals. This may include, but is not limited to, providing instructions on how to assemble bombs, grenades, and other weapons, and creating "Crush" sites;

(p) use your home page (or directory) as storage for remote loading or as a door or signpost to another home page, whether inside or beyond Yahoo! GeoCities;

(q) have multiple Yahoo! GeoCities addresses that are within the same Yahoo! GeoCities neighborhood or that have the same theme; or

(r) collect, transmit, or store any type of adult, mature, or sexually explicit content; or

(s) engage in commercial activities through the Yahoo! GeoCities service. This includes, but is not limited to, the following activities:

* offering for sale any products or services;

* soliciting for advertisers or sponsors;

* conducting raffles or contests that require any type of entry fee;

* resell, rent, or otherwise receive consideration for placement of any creative material (e.g., no third-party advertising)

* displaying a sponsorship banner of any kind, including those that are generated by banner or link exchange services, with the sole exceptions of the GeoGuide Banner Exchange program and the Internet Link Exchange; and

* displaying banners for services that provide cash or cash-equivalent prizes to users in exchange for hyperlinks to their web sites.

You agree to indemnify and hold harmless Yahoo! from any claims resulting from the use of the Services which damages You or any other party. Yahoo! reserves the right to investigate You, Your business, and/or Your owners, officers, directors, managers, and other principals, Your sites, and the materials comprising the sites at any time. These investigations will be conducted solely for Yahoo!’s benefit, and not for Your benefit or that of any third party. If the investigation reveals any information, act, or omission, which in Yahoo!’s sole opinion, constitutes a violation of any local, state, federal, or foreign law or regulation, or the Yahoo! Policies, Yahoo! may immediately shut down the site, and notify You of the action. You agree to waive any cause of action or claim You may have against Yahoo! for such action.
References :
http://smallbusiness.yahoo.com/tos/tos.php

More than whether Yahoo Geocities allow the placement of ads, it is against Google Adsense’s Program Policies to put Adsense ads on the same page as ads from competing companies especially those that mimic the look and feel of Adsense

Geocities free version puts in Yahoo Publisher Network ads — a competing service provided by Yahoo that looks exactly like Adsense

—————————————–
Competitive Ads and Services https://www.google.com/adsense/support/bin/answer.py?answer=48182&ctx=en:search&query=program+policies&topic=&type=

In order to prevent user confusion, we do not permit Google ads or search boxes to be published on websites that also contain other ads or services formatted to use the same layout and colors as the Google ads or search boxes on that site. Although you may sell ads directly on your site, it is your responsibility to ensure these ads cannot be confused with Google ads.
—————————————–

Given that free Geocities show YPN ads that look like Adsense, NO — you cannot use Adsense on the free version of Geocities (but you can use it on the paid version which does not show YPN ads)
References :