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.