Is it possible, in an ad request from
a browser to a third-party provider,
to include profile data in the request
in order to get an appropriate ad?
In general you have to inform your users (by law) that you give away their information to 3rd parties, (it's called 'privacy' ;)). Though in general, it's not done at an individual request basis. Websites sell ad-space to ad agencies who sell this space to advertisers. As websites have a given set of aspects, the advertisers buy X pageviews with sites which have aspect A, B and C for example. Ad agency then controls this: the website calls (usually in an iframe) the ad agency's ad server to provide an ad for aspect A, B and C and the ad server simply serves up an ad.
As it's an IFrame, the ad-agency can track the user through cookies, its OWN cookies. This is more valuable as they can track a user across multiple websites they server the ads for (so they can see which sites user X visits and for how long/which paths this user follows over the pages and combine that with the info the website passed to the ad-agency's ad servers in the iframe request.
The more YOU are giving out to 3rd parties (and you've to provide that info to your users) the more users will either block everything on your site which comes from 3rd parties or simply go away. Respect the privacy of your users. It will give you more in return than some big-brother deal with an ad-agency.