Social signals are contextual to the time frame when the content was shared, the medium used (i.e, Tweeted content, Google Plus shares, embedded content, social share plugins) and the share momentum (how many people tweeted the content from the time it was posted) adding up to a complicated mess of social noise. How relevant and useful your content is perceived by the search engines relies on having diversity in your social signals. All of these factors are weighed together when taking into consideration the indexability of the share. Twitter has an agreement with Google where Tweets are indexed on the SERP. Posting irrelevant links or spammy text will not be rewarded with organic traffic to your site.
Content indexation is one of the key principles of SEO. The faster you can get content indexed, the faster you can increase chances of gaining organic traffic to your site. Facebook posts, Tweets, +1s and other social signals are another layer of indexing and linking content.