You would think it wouldnt matter. Being a resident of MN I can buy tags/license for any state as long as I have it. Thats been my experience up to this point.
The only thing I’d look up and know for sure is will the state you intend to hunt in honor the safety course for any special hunts. For example, some states have special youth deer seasons.
I don’t know that it’s an issue, but I’d find out before you put time into a course in a different state.