Yes, it does count and the influence will only increase with time. AS nomis5 said Google added Social stats in Analytics. Even Google determines the Author's authority in a niche and depending upon that the link passes higher or lower weight in overall domain authority. I will suggest that you should include Google Plus along with FB towards your social media efforts of not other channels.
I will suggest that you should include Google Plus along with FB towards your social media efforts of not other channels.
eeek. Before you rush head into the social media craze know that you will not be penalized for NOT having a social presence. Conversation about your site will happen in social circles anyway even if you're not actively participating on those services to create a following. Don't confuse following with mentions, analytics reports mentions.
I believe that if you don't intend on spending considerable resources promoting the social profiles you had best not associate a profile with your site at all. No social profile is better than an unused profile. Not having a social profile of your own does not mean you can't add badges to your site for others to discuss your site without an 'official' site profile to follow.
The +1 button is a web beacon for Google 100% of the time, it's how they roll. Don't believe me? hover over the +1 button at the bottom of this page, if you're logged into Google this page knows who you are. If you're not logged into Google it just records your IP and STILL knows who you are later when it sees the IP log into adsense or other Google product.
Note: the twitter button on this page is doing the same thing but there IS a static alternative. Do as you please, but be informed!
I agree with Sgt_Kickaxe. Let other people talk about your sites on their own. I'd rather spend my time researching and writing. I don't have any social buttons on any of my sites and never will. I don't have a facebook page or a twiiter account. It's possible that I have a Google+ profile, but even if I do, I've never seen it.