No application server is needed for applets.

I would assume that you must be able to run applets from geocities. Your browser just needs to find the class file, then it gets downloaded to your pc, then your virtual machine (within your browser) runs the applet.

You may not be able to "develop" the applets at a geocities' account, because it's like uploading any (html) file. If you had a shell account at your web host and you actually compiled the files there, then you'd have to set the classpath at that site, but all the browser needs is the url to find the class file to d/l and run on your browser.