Nope ... TT gets no additional information once the return is accepted for processing. After that the only the fed/state websites have the most up to date information on the return.
TT does not update after your return has been accepted. Your account will always show the result of the return you prepared using the software. TurboTax never knows if you received your refund —or if how, or when you paid tax due. Your proof that you paid your tax will be your own bank/credit card records.