Yes I do that to squeeze my lats together. I had issues with upper-back tightness as well, and here is the exact advice given to me by a very accomplished bench presser.
Another thing that has helped me is getting good friction between my upper back and the bench surface. I would sometimes have an undershirt on, and the extra fabric made my back slide up. Going to one layer of cotton fabric fixed that. Even if I'm sweaty, I can still dig my traps right into the bench. Once I got my traps dug in I'd get my whole body tight by creating tension with my legs.
Applying these cues and really working on tightness took me from being a pretty crappy bencher to a mediocre bencher.
Head-to-toe tightness is what you're going for here.