You said that this is a varmint hunting rifle. As such, it may need to print the first shot at the same point, regardless of how the forend is supported, the weather, etc. If you fired the rifle from the same rest, the rest at the same position on the stock, and without any sling pressure, it may not make any difference whether the pressure point is there or not.
However, I've hunted varmints, albeit with wooden-stocked rifles, but have found that point of impact varies less, regardless of how rifles are supported, if the barrel is free-floating. For varmint rifles, when you don't have a lot of shots to correct for p.o.i. changes, free float if you can get acceptable accuracy. If you're shooting lots prarie dogs and p.o.i. for the first few shots aren't as important as group size, that may be a different story.
For the record, I've never found a centerfire rifle that shot better with a pressure pad. That doesn't mean that I didn't have to change my seating depth to account for vibration differences, but I usually just free-float and bed a new rifle, then work my loads up afterward.
Picher