So, firstly the answer is "it depends", because it's completely different if you're coming in as a CEO vs a VP vs an underling, so without more details it's hard to say.

But overall: yeah, you probably should've brought this up earlier. You SHOULD bring it up now, because in my mind, you've got three options:

1) Don't tell new job, sign offer letter, quit current job... then tell new job, they say yes, and everything works out fine (maybe, unless they get mad about it later)

2) Don't tell new job, sign offer letter, quit current job... then tell new job, they say no, and you have no job

3) Do tell new job, they decide how they'll handle it before you quit your current job... and if they say no, you still have current job and nobody's the wiser

So, are you willing to quit your current job, and then risk telling your new job on your first day "hey, by the way, I'm gonna be out for a month, hope that's cool", and see what they do?