I think that google now uses a headless browser. Unless your page loads in too much time, nothing should change on the SEO side if you have the same content at the same place.
From what I've heard they do, but not for all of it. The bulk of the crawling is still done without it, and some subset of pages (probably based on some detection of "this site requires JS") is crawled with the more expensive, JS-enabled crawler too.