Would a supplementary civilian course be necessary in addition to the standard military deal?
No. If you have received the standard Marine Corps safety classes from your AMOI, you will be good to go. I don't know where you're going to school, but if you're at A&M, you're going to have access to resources not readily available to most civilians. 4 basic safety rules...Go ahead and memorize them now, because you'll need them at OCS and TBS, thankfully regardless of MOS.
1. Treat every weapon as if it were loaded.
2. Never point a weapon at anything you do not intend to shoot.
3. Keep your weapon on safe until you are ready to fire.
4. Keep your finger straight and off the trigger until you intend to fire.
My roommates and I used to keep condition one weapons in the house without incident, and we were comfortable with it, as long as no guests were in the home. As soon as the guests showed up, we briefed them and made sure we didn't leave them unsupervised in the rooms that contained the weapons...
Safe weapons handling is a perishable skill though. The more time you carry and fire your weapon, the safer you will become, as you develop muscle memory. If you have long periods between the times you handle your weapon, you will forget basic things. The safest and most proficient I ever was was when I was carrying a weapon every day, 24/7. You won't be able to do that at school, but make the most of the opportunities you do have, and look to create opportunities when you can.