I didn't recomend it, just looked in the regs and it does not have a max caliber you can use on them, but it does say that all you need is a small game license to be legal. 
Except during hunting Deer/Elk season. It states this specifically. you must have a deer/elk tag if the gun is bigger then .22 cal during the respective seasons
Yes you are correct. It didn't even cross my mind about hunting grouse during big game season, guess it should of though.