No, but it makes shared links less inefficient. If you share a URL like this, the server will not receive the hash on the initial request, so the js client will have to do the search as a second request after the page load. The reality is that most users will never even notice because it's still fast.
Manually editing the link causes that same fetch-render-refetch flow.
Edit: Oh, you were asking about pushstate. No, that specifically fixes the problem with the double fetch, so long as the server side and client side do the right thing to make the user see the same page for the same URL.
Pushstate just lets the JS client modify the URL without triggering a page reload, so the client can change the actual query param instead of the hash.
