If you're from a country that has been authorized for TPS status I have seen plenty of nationals with TPS apply for Advanced Parole=Travel authorization.There are separate designations for each privilege.TPS basically allows a person to stay inside the US for specific humanitarian reasons allowing one to apply and gain an EAD through the status but one must be approved separately for Advanced Parole.

There is also no guarantee that one can return to the US on AP.Only US citizens and Legal permanent residents[/w no criminal record] technically have a right to return.