Yes, server side scripts (PHP, .NET, whatever else) do transform data into HTML before returning it to the client. My question is whether Google Analytics indexes the entire page contents every time the pages loads. I doubt it, and therefore I doubt it can be used to track what he's looking for.
Google Analytics does track URLs. Let's say when a user submits a search form, the target page puts the search term in the URL--something like this.
I know that Google Analytics will keep track of the number of visits these pages. What I don't know is what they do with URL parameters (i.e., everything after the ? in the URL). If it strips those, then this approach is useless, but if it keeps those it may accomplish what you're looking for.