It's a complicated answer, but yes and no. A pilot needs to warm up in order to pull the high Gs as rated by the airframe. In addition, you can only pull the rated G-force for the plane for so long before blacking out. In addition, the plane has to be re-certified after going over a certain G rating.
I recall hearing that yes, they could, but it will wear out the airframe faster. Like all engineering projects, they are designed within constraints. Of course this is frame dependent, but it also means new airframes designed without pilots in mind are now possible.