Yes, you can spend the day in another park. You don't need hoppers to do that since the party ticket is freestanding.
We have opened and closed the MK on party day many times. I prefer building lots of breaks into our day to rest and be off our feet in the park to going back to the resort. But there are no young children in our group, and nobody ever naps. For some reason going back to the room just makes me more tired. I prefer to find a nice spot to sit and people watch. And we always did a nice ADR (usually CRT) around 4:15 as a natural break, then came out from dinner and sat in the line for 7DMT so we ended up off our feet for more than a couple hours.