By retweeting and replying to fans, and sharing his random thoughts on space travel and cats, followers get to form a relationship with this artist on a level that would be highly unlikely if it weren't for social media. As Mark Schaefer constantly alludes to in his book Return on Influence, effective marketing on social media is all about building relationships (Schaefer, 2012). By interacting on social media, brands - whether that brand is a corporation or a rockstar - can have an added human element, and seem more connected to the consumer.
From a business perspective, I imagine this could only help Ryan Adams' cause. Interacting on Twitter keeps him in the consumer's mind when he's not touring or promoting a new album, and gives him the ability to easily update his followers on when he does start touring or recording a new album. Followers can also get perks from these social media relationships as well. I once won a pair of tickets to see Ryan perform Live on Letterman - separate from the Late Show with David Letterman - it was an hour-plus long performance in the intimate Late Show studio. Ryan Adams' official Facebook account posted an e-mail address and said the first x-number of fans to e-mail the account would receive free tickets to the performance. It's things like this that attract new fans (consumers) and keeps the old ones around, and hoping for more.

UPDATE - 3/7/15: After incorporating my personal Twitter, Facebook and Instagram accounts into my Klout score, it is now a 51.27 - not too shabby!
--------
Source
Schaefer, M. (2012). Return on influence: The revolutionary power
of Klout, social scoring, and influence marketing. New York, NY:
McGraw-Hill.