Surgeweb google AdSense advertising can be enabled in a right colum in the interface by setting the "right_column" content setting and then customising "ad1_html" to contain your google Adsense string "all on one line".
First a warning: Surgeweb is an Ajax web application and only has a single page refresh at the point of session login. Google AdSense is not very well setup to work with Ajax applications as the googles policies basically seem to state one display of adverts is allowed per impression. Where an impression is a full page refresh thus one refresh per surgeweb session. This seems unreasonable and all ajax application fall under the same category - including gmail.
Surgeweb has has settings that will allow the google ads to be updated on display of new folder contents, display of messages for viewing or for composing / editing. These are pretty much the points at which a full page refresh would occur if surgeweb had not been implemented using ajax. I am no legal expert and I don't know whether you will get in trouble with Google if you use these settings, but I would have said there is a reasonable case for "fair use".
Anyway, as now setup in surgeweb there are two settings that can be configured on the surgeweb customisation page in surgemail:
Set to 'rotate', the ad banner will rotate on the interface actions described above but no targeting of the ads is attempted. Dependent on your website this will provide different ads but in my experience leans to many "electrical surge protection" ads as "surgeweb" is part of the url. That also might just be my test server has not been crawled by google, but google should never get much by trying to crawl surgeweb pages. Maybe the higher level pages??
Set to 'target_simple' this will step through each of the ad1_keywords words when updating the ad banner, and use it as part of the "site url". This should provide a basic level of targeting, although there seems a fair bit of black magic in what google displays.
Set to 'target_subject' will try and use the message subject to target the message for clicks opening a message. Other clicks like folder clicks will default to the ad1_keywords defined words, and without that default to whatever google serves.