Not in the case of my Holland & Holland .470 NE. It makes no difference in shooting off-hand standing or shooting the rifle over a rest while standing, absolutely zero. And I shoot my gun well enough by now to confirm this (off-hand my groups are between 1 and 3 inches when I take my time aiming, over a rest a consistent 1.5 inches) I get absolutely identical results - there is even not much difference when putting a scope on. And there shouldn't be, as manufacturers clearly regulate with the rifle resting on a pad. I have a picture of how Holland & Holland regulate doubles and will post it.

However, when shooting seated, regulation changes dramatically, irregardless of whether the gun rests on a pad or on ones hands. Obviously, how the body reacts to the recoil (seated versus standing) makes a difference, not whether the gun rests on the left hand or a pad. Having the rifle on a rest, rather then sitting in the left hand which then sits on the rest makes for a more consistent set-up, that's why manufacturers regulate like that. Picture of Holland & Holland regulation shooting to follow.