If you're caught out with deer hunting gear, license, etc., and a gun that is not legal to hunt with, then you will face whatever penalties that state has set up for that offense. You don't even have to be caught shooting anything, just being out in the season with what appears to be hunting gear is enough to get nailed.
In some states, you can hunt deer with .223 but pretty much nothing smaller. There are a ton of other rules which is why even if someone is exempt from the hunter safety course in a particular state, they probably ought to attend a course anyhow just to brush up on the applicable laws.