NO, it is strictly forbidden to let go of your padel to play a ball. It's not not regulatory.
For example, if you try to catch a high ball by letting go of your racket, it is prohibited.
It is imperative that the hand be glued to the handle from la pala. Otherwise, the ball is foul.
La International Federation of Padel (FIP) is very clear on this point and it is the coach Raphael Galvez which reminds us of this very important point.