Yes, they (or some) do celebrate there birthday.
Ajahn Sumedho celebrated his 72nd (?) a few years ago, and the Abbot of Chithurst celebrated one while I was at amaravati, many of the monks and laymen went there for it, I didn't so don't know what went on, wish I had, but I didn't want to go there for the occasion when I didn't know him!
I also heard from one of the lay guests who used to be a monk at WPN about times he visited (with others) famous monks (in the wider forest tradition) for their Birthdays, but he mainly talked about them as inspiring people rather than the celebrations.
Blog, Suttas, Aj Chah, Facebook.
He who knows only his own side of the case knows little of that. His reasons may be good, and no one may have been able to refute them.
But if he is equally unable to refute the reasons on the opposite side, if he does not so much as know what they are, he has no ground for preferring either opinion …
He must be able to hear them from persons who actually believe them … he must know them in their most plausible and persuasive form.John Stuart Mill