I don’t think that hashtags are a search only feature. In the posts themselves, the hashtags are clickable to view other tweets. I don’t think that qualifies as a search.
It does strike me as a feature you'd typically serve out of some sort of search index since if you had to build search, you'd essentially get indexing of hashtags "for free"
You are probably right and I am wrong. I just looked at a tweet and clicking the hashtag takes to the search page with that hashtag typed in. Probably implemented similarly behind the scenes. Though hashtag most likely does an exact match search instead of fuzzy searching for regular words and phrases.
