YES! I ran in/around the parks yesterday morning. If i need to do around 6, i run the perimeter and then end with and out and back from the harbor side entrance to the DLH and back. It brings back all the feels from running through DTD for runDisney events. You will have to go through security—twice if you do the loop around the hotel. On previous trips, I never encountered security. This year I did—like 3 hours before park opening. I think they are used to runners. I ran past bag check, there my phone on the table and then grabbbed it as I passed under the metal detector. Have a magical morning all around! If you need a shorter route, the run along Katella is nice. Harbor is great, just a lot of stop lights. I’ve run through neighborhoods and even made my way to the reservoir a few times.
Any route you choose, it will be fun and you will encounter several other runners. Enjoy!