Ask HN: Tf-idf search index vs. brute-force Doc2vec and query comparison

If on one hand, we have a classic search index with ~tf-idf based scoring algorithm (a well configured elastic search, let's say). And on the other hand, we have a list of document vectors generated for every document, using some sort of modern, semantic-aware Doc2vec algorithm (a-la word2vec). Now, if we completely omit the speed concern and for the second case will just iterate over every document and calculate a distance from it to a query vector and then pick N closest as a search result. Is it a common sense that these results will definitely be more relevant to a query than those, obtained from a regular search engine? Or will the improvement be just marginal or not better at all? Can anyone point me to an existing experiment with some real numbers available?

Also, am I right that the second way should do things like matching "health insurance" to "employee benefits" and "SF taxi" to "California transportation" kind of out of the box, assuming that the "Doc2vec" is well trained and produces rather large vectors for every document (or let's even assume we only work with document titles and hence rely on "Sentence2vec").

I would be really grateful if someone could shade some light on this area of information retrieval for me. Thanks!