We have done this and it is not a problem. However, having a cameraman in the jump seat is not the way to go IMHO.
We had one lipstick camera (small camera size of a lipstick container) mounted on the dash, and 2 other cameras mounted in the top right and left ceiling positions behind the pilots looking at each pilot. Also had it hooked up to a taping deck which was securely mounted near the rear door.
Actually made an interactive DVD for training purposes of checklists etc. Works well.