It sounds like you're asking for "Google Instant" functionality on StackOverflow.
I think it may be cool, but considering the nature of StackOverflow, users may use advanced search syntax which might confuse the results as the user types. If I search for
user:me is:answer, how would the advanced syntax play out?
Also consider the number of server requests that will happen vs the number of wasted requests. If I search for "
XMLHTTPRequest", then the first three "pings" back to the server are wasted because my fourth character drastically changes the meaning of my search. Going back to advanced syntax, the problem becomes even more exacerbated.
In the general context of Google this works. In a specialized site where many searches are likely to use advanced search modifiers, I don't think it's as simple. I reluctantly (and politely) say no.