I am wearing a cast for complete breaks of ulna\radius. is it possible to displace the alignment of the bones while wearing a cast?

A fracture can move : Or shift due to the pattern of the fracture ( some are inherently unstable) the quality of the bone, the energy of the injury ( higher energy injury that was more intially displaced) the amount of initial reduction and other variables . This is why a fracture needs to be followed once it is casted, repeat x-rays, cast changes are all a part of this. Fracture care is mor than just the first cast.

Yes, absolutely : A cast provides some protection and stability to a reduced fracture, but the bones can still displace - especially in the first 2-3 weeks. Plates and screws are better at stabilizing the fracture. Things that you can do: follow your doctor's restrictions regarding use of the arm (no lifting, etc), follow up regularly for x-ray, keep the cast clean and dry, change your cast if it become loose.