At this time there is no current production truck having a convertible top.
With a body on frame, unfortunately I don't think the battery is going to help the body stiffness that much. They would still need to do a lot of reinforcement in the cab itself.I love convertibles and I love trucks. Not sure the two should ever be the same vehicle, though.
A clamshell top for a supercrew cab is going to be huge and unwieldy. It'll also take up almost the entirety of the bed when it's down, but I guess you'd just put the top up when hauling.
Structural integrity might be better on the next gen Lightning BEV with the dedicated EV platform. That'll probably have a structural battery pack.
The frame is the structural member, and would only be stronger with a structural battery. They would do some stiffening of the cab, and include a roll bar as @MudDog has done. But I realized after my earlier response that removing the roof really doesn't affect the vehicle much in a pickup. The cab only has to support its own weight and that of the passengers. It's not like a sedan where the roof adds to the stiffness of the frame (or, in most modern cars, IS part of the frame).With a body on frame, unfortunately I don't think the battery is going to help the body stiffness that much. They would still need to do a lot of reinforcement in the cab itself.