It would be like shooting a 270 Win out of a 30-06, could be done but would be worthless.
To give you an example, I was running our clubs "sight in days" just before last years hunting season.
One lady shows up with a nice Remington '06, and couldn't hit the target at 100 yards. She got up sit, saying she shoots better then that and so does the gun.
After a bit I convinced her to shoot at 25 yards to see where the bullets were going. She missed that target twice with 2 rounds, hit with two rounds, both keyholed.
Turned out her hubby wasn't paying attention, picked two boxes of ammo, one in '06 and one in 270. When this lady switched to the '06 ammo both the gun and her had no problem grouping and the rifle was sighted it.
So if I was to shoot a 358 Rem, I'd go a head and buy 358 ammo. You might get 308s to fire, by you wont hit nothing. Better off staying home.
CPT USAR Ret
USAMU Sniper School Oct '78
Distinguished Rifle Badge 1071