Is the tonneau cover hard, soft, roll up, folding?
I use a guide gear bed tent now but no cover.
If your cover is hard you'd have to disconnect the shocks and lift and secure the cover vertical. With the folding ones you may Be able to do it if the folded part will lay up against the rear window. Soft Rolling ones you should have no problem.
It would be easiest just to remove the cover at home when you want to use a bed tent.
I used a bed tent (floorless) with my tri fold for a year. The tent was not a perfect fit but well enough to stay dry. It was OK in good Wx but it flapped a lot in windy rainy nights. I ended up with a Softopper and drawers. I carry 2 totes I need to unload, camp chair and table, this takes a minute and camp is ready. I have a tarp I can put up on the end of the truck when the Wx is bad. Camp setup or tear down is under 5 minutes, I spend my time moving, not sitting in camp.