I fucking love Adam Driver. That needs to be said right away.
Other than horror movies, rarely do I get to be the guy in my peer group that catches on to a talent first. I saw Adam Driver in Girls and thought he was absolutely spectacular, and have had no one to tell about it for years. Since, he's been in This Is Where I Leave You, which was a delight, and the recent Hungry Hearts which was the opposite of a delight but totally awesome. There were other less significant roles to be sure, but these two seemed to ignite a fan base.
Oh, and Star Wars I guess.
I thought Adam was good on SNL. My wife said something poignant beforehand when I said I was nervous for him (which is completely ridiculous but exemplifies my level of fandom). She said, "I can see him being the sort of guy that they don't know how to write for." I think she might have been onto something. Though Adam was competent to great in the sketches, some of them were host throwaways like the football announcer and the partying father. And then there was the porno sketch where he was great, but the jokes were written such that anyone could've pulled that off. Overall, I think he did a good job. Aladdin (due to Cecily Strong) and Undercover Boss were highlights for me.
Short Answer: I think he'll be just fine.