It is my understanding that turkey beards grow about 4-5 inches per year. So best case scenario is a bit under 1/2" per month (about .42")...
Of course diet and habitat can play a role on beard growth as well, and I would suspect that there are times of year in which beard growth occurs at more or less rapid rates depending on food supplies and bird behavior.
First bird I killed was a jake with a 7-8" beard... An unusual situation, and I would guess the bird was born early the previous spring (I identified the bird as a jake due to the uneven tail-fan)... Jakes with longer beards were probably hatched early, and birds with shorter beards hatched later.
Last year we had some late sring/early summer storms and there was an obvious attempt of some birds to re-nest... I would guess that if we had as good as a hatch as I suppose, I will see some jakes with varying beard lengths (I have not actually seen a jake at all in my area in the last 2 seasons).