No. We do see a brief flashback in one of the more recent serials dealing with the Master, that shows that all young Time Lords, as part of their initiations, look into an unprotected bit of the Time Vortex, which has an indelible effect on them (driving the Master world-dominatingly mad, and Doctor... Well, apparently just mad in general :P). I don't recall if we see the Doctor himself, but we did did a young Master, and he looked like a normal child.
So I think we can assume that however they are born, they are not born as "old", they grow up into it, and then if they regenerate, it's a bit of a crapshoot, whether they will look the same age as, older than, or younger than their original body (see: River Song, who regenerates from a 20-something body, into a "mature" one, and the Doctor himself, who's been regenerating into somewhat younger-looking bodies as of late).
There are implications in recent Series (forget where, exactly) that the Doctor has only regenerated 10 times, which would imply that he got his elderly First Doctor visage the old-fashioned way: by aging into it. ;) We do know he was at least a couple hundred years old by then, so it's not terribly implausible.