There should be no problem if you install the right receiver hitch on the TV. The opening of the receiver should be flush (or nearly flush) with the back of the truck, whether the "back" is a bumper or the bed. If your receiver is not flush with the back of the truck, you can add an extension of the right length to make it flush.
Buyers Receiver Hitch Extension 1804005
But an extension will reduce the weight capacity of your receiver, so you may need to install a different receiver that will have the opening of the receiver flush with the back of the truck bed. Or maybe a heavier-duty receiver that will still have enough weight capacity when the receiver extension is used.
Assuming your current pickup bed is 8', then the flat bed is 6" longer. About the same distance a step bumper sticks out behind the bed of a pickup.
Your truck probably cannot turn sharp enough when going forward to cause truck to trailer contact. So backing is your concern. If you disconnect the WD spring bars, you can back into a jackknife that might allow truck to trailer contact - at the rear corner of the bumper or the rear corner of the bed, which ever sticks out behind the most.
So if experience says you cannot back into a jackknife without truck to trailer contact, then either put up with it, or replace the receiver, or add a receiver extension.