It can be done.
If you are willing to put in the time with consistent training you can have your dog loose on the course chasing his discs while you play a round of golf. The good news is you have a very smart dog and "training" is playing disc golf.
I have a 4 year old Golden retriever/ standard poodle mix (goldendoodle if you will). And I bring him with me to almost every non PDGA event round I play.
The key for me was establishing his discs. The ones he can fetch, and leave all others alone. Easier said than done. So heres a few tips getting started:
1. Always have 2 dog discs: one to go fetch, and another to hold up to encourage the dog to bring it back. This discourages them from trying to play keep away.
2. Treats, treats and more treats to reward positive behavior. Especially if he starts to track another disc but backs off on your command, that is a key one to reinforce.
3. When driving I started out with the leash wrapped around the tee sign, to keep my dog from running after my drives. Then after I drive I will throw him his disc, a few times as I walk up to my drive. I also like to throw his disc as far as I can out of sight while putting so I can concentrate on a putt.
4. Start on a quiet course, or go when there are few distractions: this is going to take some time, and you will probably have to replace a few discs for other golfers that your dog picks up and punctures. So go to a quiet course or go early in the morning to start.
Good luck, it is a lot of fun to have a dog that you can trust on the course.