Depends on what "really high level" is to you. Is it being a virtuoso making studio recordings and selling out concert halls around the world? Or, being able to play difficult music for your own pleasure, friends, family, and maybe small recitals? The former, I would say it is not likely. But, if you have a musical background and start "older", you can still play at a high amateur level.
I started older (16), but had a musical background and picked it up quickly. Do I wish I could have started earlier, absolutely. I'm now 32 and I find I can play pretty much whatever I am willing to spend the time on, but not being a professional, finding the time is what will limit you.
Don't let potentially not being a virtuoso stop you from learning, though. I think everyone wishes they could be out concertizing in front of thousands, but its probably not as romantic as it sounds. Check why you want this ability in the first place. Focus on doing it because you love the music and the connection that only playing an instrument can give you. Its a life long rewarding process either way.