There is already any "Age" field on the profile, which you are correct in that it needs regular updating. I think this is easier, though, than putting a birthday and having everybody do the math to figure out just how old your character is.
It would have to be one or the other, in my opinion. Otherwise, if for some reason they contradict each other, people wouldn't know what to go with.
I also don't like the idea of a "Birthday" field for your characters as there is already a "Birthday" field required by law for you to register on the board (as per
COPPA). Differentiating between the two could be confusing for newer members. I've already had to code in to the board an alteration of the existing profile field so it is made clear that it is OOC. If that confused some well experienced members in the past, this could confuse some new ones.
Regardless, I am open to the idea if a significant number of people would prefer it to the "Age" field. I would advise against it, but if people want it instead they should indicate so here.
Otherwise, my answer is no for the reasons stated above (and I hope they make sense to you).