I think this makes sense, though 200 might be a bit on the low end. I think it's possible that after a while he'd just stop keeping track of birthdays (or days in general), especially since he really has no reason to keep a Gallifreyan calendar around. I mean, we see this from Amy and Rory's final arc in Season 7. They go of and have random adventures, but they really have no concept of how much time is actually passing on Earth. The 200 year jump in Matt Smith's run is especially telling, I think. I don't care how old or Time Lordy you are; if you go 200 years without seeing your friends, you're not going to treat them as if you just saw them a week ago. Hell, you probably wouldn't even remember what they look like.
Actually, funny thing, I've always felt the reverse, that his life is so fast paced and frenetic that he doesn't realize how much time has passed. I've frequently said Nine could've lived for 100s of years before meeting Rose and just never slowed down long enough to see his reflection until he meets her. I just can't imagine anyone travelling through time frnetically and constantly bouncing from one adventure to the next for years (or centuries) and having any clue how much time has passed. As you say, Amy and Rory don't feel like 10 years has passed, but they know it has from their friends commenting on their aging.
Baised on on-screen and dialog evidence, I would guess that the answer is *YES* - but at a much slower rate than humans. The 11th Doctor went from "900" (though I think he was lying about his age then, he should ave been older) - to 1100...and then some. All looking the same. But as pointed out before, the 7th Doctor did seem to age visibly by the TV movie.