Hi,
Technically, it could be feasible. You have to introduce 'budget period' as FM object and put your budget on this assignment along with other FM objects (fund centre, commitment item, etc.) By this, you will achieve control on monthly level.
Now, for the more tricky part of cumulative control, I believe, you will be able to achieve this with 'cover eligibility' functionality, creating a pool, which would check budget in budget periods, which are equal/below the month of the posting.
Regards,
Eli