As long as the truck frame is not bent too severely and the truck drives straight enough then yes you could drive the truck with a bent frame.
I've driven trucks before with bent frames that were in crashes and they were still safe to drive and they drove pretty straight.
However sometimes the truck frame may be bent enough and cause the tires to not track straight and be out of alignment which could cause the tires to wear unevenly.
But if the truck is driving okay then it can be safe to drive the truck with the bent frame.
You can sometimes have a truck frame straightened out by a body shop that has some equipment to straighten the truck frame back out if it's not too bent.