Yes, you can operate a shotgun so long as you abide by state law. However, if you were to be accused of a marijuana related felony, you'd be screwed. I'm sure your wondering how you could possibly be accused of a drug felony while a medical marijuana patient. Its actually not hard at all to commit a felony.
A couple examples;
If you were to be caught with more medicine than the law allows. (Possessing 16 Ounces in a County that only allows you to possess 8 )
Or maybe you were caught medicating while driving down the highway.
Selling your medication to non-registered patients.
Any of the above examples, when combined with possession of a firearm, will likely end up in more serious charges.
Assuming that you are a legitimate medical patient, following all the laws and rules, you can retain your right to bear arms at all time.