Yes, very recenly I had this experience.
There is a 3 day difference between my wife's and my schedule for
finger-prints.
So I called the Vermont center, to find out if I can get the fp's early.
Then they said go to the Newark center (which I planned to go anyway,
with my wife) and try if they take it.
At the Newark center, initially they said they can't take mine, as they are
too busy. But then, they decided to take anyway.
So, it is okay to give the fp's early. But generally they will not take it, as it would affect their schedules.
Thanks.