No - nor would you want to. Anything heavier than one of the utility trailers you buy at Lowe's or Home Depot would put too much weight on an extended draw bar. If you have a weight distributing hitch, that also wouldn't work. If you don't have a locking Tonneau cover with the need to lock the tailgate for security, you might consider a fifth wheel tailgate with the notch cut-out. It would keep stuff in the bed but you could lower it with the notch clearing the electric tongue jack. I had the same complaint when we pulled a travel trailer so I understand your frustration.
Rob