Hi,
Short answer is that Social signals are not used for rankings at all. (if you think about it it make sense since you can fake those like there is no tomorrow).
Read more on this at: http://searchengineland.com/googles-matt-cutts-facebook-twitter-pages-are-treated-like-any-other-web-page-on-the-internet-182370
On the other hand, if you do have a large exposure / visibility on social networks, a real one - not faked - with real users and real interaction chances are high that people will share, quote and link to you and that will impact your SEO efforts. I would not focus on social just to get SEO advantages though as it will prove to be a negative ROI.
Related with your last statement - it's true that once you +1 or share on Google plus or twiter for example an URL chances are high that you will get indexed faster - note that there is a distinction between getting indexed and getting ranked. Google bot will find your domain / url faster, it will crawl and index it but that doesn't mean you will rank, rank well or get any boosts in rankings - you are just in the index.
Hope it helps.
Cheers.