Well, I guess I may be misunderstanding but if not, I was under the impression that the OP was using the same shooter, rifle and load with his 3x9 scope and wondered if his groups might not get smaller with bigger glass. Do we agree that this is paraphrasing his initial question?
While I am sure that it will not guarantee anything, I am just putting forth that if he were to put bigger glass on the same rifle with the same guy behind it and the same load on the same day and shot say, 10 5 shot groups with each scope, one 3x9(or whatever and one much larger(say 8x32) at the same wind free tunnel in Texas that its my guess that his group size would perhaps go down in size ceteris paribus.
Does it make his rifle more accurate? No, if that were the case every time some one shot out a barrel they would just bolt on a bigger scope and those one hole groups would just magically reappear.
To play a bit of devils advocate, I also believe one could shoot better groups with a real high quality 3x9(Leupy, Zeiss, Swarovski...ect...ect than one could with a 69.00 25x piece of junk from Cheaper that Dirt.
Maybe distance needs to be factored in. Maybe at 100/200 yards the power thing is not such an issue but what about at 1000 yards? The Op never mentioned distance or I might have missed it too.
Anyway, All I know is that in load testing my 5 different coyote rifles, I put on a VX2 in 6x18, do my testing, find a load the gun likes, then switch scopes to my 3x9 VX2s for hunting situations(trying to find a running coyote in a 6x18 scope turned all the way up at 50 yards is an exercise in futility most days) and they just dont shoot quite as well because I cant see as well.
Anyway, I am no expert by any means but thats what my humbling years of experience has shown me.
Jamie