I was one of the first french seo consultant to switch to SSL in france, i have seen a significant long tail effect in terms of SEO in a couple of weeks after i switched to it. Other french SEO agencies that followed me saw a significant jump in SERP positions too.
Only my long tail keywords were significantly affected, the "big ones" did not gain anything, but also it might be because it's a "nuclear war" on the french equivalent of "seo agency"/"seo consultant" etc.. I'm managed to rank very well with "french seo agency" on an international level, and i don't think i would have succeeded without https, it gave me that little extra ounce of power i think.
You can have part of your site in https and some other parts in http. But beware, google considers https and http like 2 different sites, so make sure to make all your 301 redirect properly else you risk of losing lots of link juice and then your positions...