Bots that pay attention to the robots.txt will not visit any URLs that are blocked, so the pages won't be deindexed.
As for how long to wait, I'd hold tight until all existing results have disappeared. I don't know how big your site is, but I had to noindex search result pages for a site I work on. I'm on week 18 now and there's still a few lingering pages.
Just do a site:example.com/searchResults.php in G and wait until there's no more results.