Is social media helpful for research dissemination?

I initially left this partial answer as a comment on aeismail's great answer, but it didn't actually fit very well. To compliment his evidence-based answer, I wanted to provide a "use case" for social media.

Why might social media be better than a search engine? Because it provides opportunities for discovery outside of time frames when one is explicitly looking. (In this way, social media functions like alerts from ArXiv that a new paper has been posted to X topic.) Because I have a Zotero (bibliographic manager) plug-in for each browser, any time I come across an interesting article, it is extremely easy to file it away for later if it is a high-quality work that fits into my broad set of interests. When I am putting together a syllabus or literature review, the papers already in my reference manager can be a good starting point for further search.

In an interdisciplinary field, it can be hard to learn about all the relevant new publications. Anecdotally, I follow people (grad school acquaintances, colleagues, researchers I admire) on social media, and I often discover references to research that is germane to me, even if it does not appear in journals or conferences I see regularly. (While some of the relevant work would be posted on ArXiv, many of the papers would not be.) Thus, through social media I'm often helping the hit count, sometimes the citation count.

A search is also tough if the terms one is interested in are broad or vary by field. In those cases, setting up a saved search to look for them may not be useful because many of the results will be false positives, and they will not be filtered for quality. (Plus when I set up automatic searches for anything that produces a large number of results regularly, I usually end up just ignoring them rather than sifting through them.) Thus if I can follow several prolific academics who regularly tweet about their own work and what they're currently reading, this helps me discover interesting work with very low effort.

Also note that most quantitative study designs wouldn't disentangle the effects of social media versus search engines. That is, one of the advantages of a social media post is that many of them are included in web search results. (Analysis of social media's effect on citations will actually under-count social media's impact to the extent that private announcements--like friends-only Facebook posts--are not included.)