The way to find out is to shoot your gun at whatever range you wish to take deer at. If, at that range, be it 50 or 200 yards, you can keep all shots within 6 or 8 inches from the position you'll use when hunting, then the gun will be OK to use at that range.
I shoot a scoped 357 Herret which has just a little bit better performance than the 357 Maximum. With that gun, I'll take an off hand shot at up to 50 yards but want a good rest such as shooting sticks or the prone position for shots longer than that. I've never shot it at a 200 yard target so wouldn't want to bet it would be accurate enough at that range for hunting.
With handguns, I've seen bullets that would give excellent (1 or 2 inch) groups at 50 yards that would only group 6 or 8 inches or more at 100 yards so don't assume good groups at 100 yards mean acceptable 200 yard groups.