I don't think age really as that much to do with it. I did't start until I was 15 and the other day I played with a 15 year old who was playing off 5 in only 2 years. Many people would kill for something like that, what counts is how enthusiastic you are.
I reckon it's mainly down to the amount of time you have available and how good a relationship you have with your teaching pro. As you get older, though, you may get less flexible which can make it harder to learn and you'll probably be a little more stuborn in your mental attitude too, all of which can hamper your progress.
Being in your 20s is not too late ... maybe if you're planning to be world champion it is, but there's no reason you can't hit scratch. Getting a tour card is going to be slightly harder however. I love playing the game and though I play to a reasonable standard (3 at the moment) it's unlikely I'll make it into the big time but I don't let that worry me too much.
Paul