I don’t 100% understand what you’re proposing.
It seems to be 2 distinct features - some special search field and some mechanism to connect queries to questions. I assume you meant questions, not answers, otherwise I’m even less sure of what you’re proposing.
If they’re one and the same, then the fact that you managed to find the question using those search terms means finding it with those terms is clearly fairly easy, so no additional changes seem necessary to specifically connect the two.
For the search field, how would this be different from a “regular” search field (or Google search)? If it’s a more detailed search field, it seems quite similar to what Stack Overflow is doing when you fill in your question (title, body and tags) and it proposes similar questions (but with the disadvantage that you presumably have to type in your question twice - once for searching and once for posting).
For connecting queries to questions, what exactly do you have in mind? How would you get from someone typing their alternative phrasing of the question into Google to actually getting the result they’re looking for? Or is this just for onsite search in case you search for something similar to the alternative phrasing? Although that’s probably not so useful as most people would be coming through Google.
Stack Overflow addresses the alternative phrasing search problem by having the alternative phrasing exist as a separate question that’s closed as a duplicate of the original. It’s not ideal, as you’re splitting it across multiple pages, but I’m not aware of any better way to do this (I would be interested in finding out whether there is one though).