In theory, if everyone had a facebook profile, wouldn't a facebook search be more useful than a google search in many instances?
I don't think the search has to be difficult to be useful. A facebook search can certainly provide more contextual (and by extension, more useful) information than a google search.
The question is, how large of a context do you want your search to touch?
I think that the size of the facebook (or myspace) user population can grow to such a point that internal search becomes a serious substitute for a more general search with an engine like google or yahoo.
I think the trend you are pointing out is already in full force: often you'll jump over to Wikipedia directly, or IMDB to get data on movies. It is really easy to make search work when individuals format their own data into a specific format for usage by your search engine. This keeps on being useful until people start abusing it. In a social app like facebook it seems relatively less rewarding to abuse the system though.
"Search engine" is an amazingly ambiguous term, to the point of being almost meaningless. It can refer to anything from a one-line SQL query to Google's system. Searching data that's completely under your control just isn't very difficult in general. When money is no object it's usually trivial, just throw memory at it. I look forward to the many clueless articles claiming this is a challenge to Google.
I think that the size of the facebook (or myspace) user population can grow to such a point that internal search becomes a serious substitute for a more general search with an engine like google or yahoo.