The short answer is yes, but it depends on the situation. For your traditional conventional loan, the bank is going to want to see those funds sitting in a bank account for probably at least two months. You could move the money into a checking account and let it season for the two months, but obviously you will be paying interest on it from day one. If you have the personal funds for the down payment on a deal, maybe you could use those funds first, then pull funds from the line of credit to refuel your bank account.
If you go with a commercial lender, some have longer seasoning requirements and some just want to see the funds in the account two weeks prior to closing. So that's an option as well.