For whitetail and typical hunting weight bows I would think 5gr/lb would be enough to penetrate unless you have a problem with shooting heavy bone. Grains per pound is not telling you what the kinetic energy or the inertia is. 5gr/lb out of a 80lb bow would be more energy than 5gr/lb out of a 40lb. Longer/heavier arrows will have more inertia than shorter/lighter arrows. Then you're not taking arrow drop and range estimation into the equation, high gr/lb won't do you any good if you're a few yards off on estimation. There is no one thing on a bow you can use as a deciding factor for its huntability.
The reason people don't hunt with 5gr/lb is that bows tend to get very noisy when shooting that light of an arrow. I stopped going lighter at 6.5gr/lb because of noise. I've since lowered my draw weight and am at 7.5gr/lb and the bow is very quiet. If my bow wouldn't have been so noisy I would've went all the way to 5gr/lb, the faster it went the deeper it penetrated into my target.
I may be outdated but I've always heard that 5gr/lb is the minimum. I know I've had bows that stated their warranty was void if anything lighter was shot. My present not so old Martin single cam manual states that. So the answer to the original question is, Yes, you are probably asking for trouble. You should consult with PSE and/or your bow manual.