Cost Center Budgets

Hello Experts,

We are trying to activate cost center budgets and here are the two concerns that I have:

1. Like Internal Order/Projects, does budgeting on Cost Center do Availability check and give a hard stop on any transactions hitting that Cost Center if there is no budget left? We want to be able to hard stop on any transactions that could go overbudget.

2. If so, there are few Cost Elements that we want to hit the cost center even if there is no budget left. Somethings like T&E which has already occured and is entered in SAP via interfaces, since we want to avoid the complication of these transactions hitting suspense accounts. Is this possible?

Thanks in Advance!

N.

PS: All answers will be duly rewarded.