Couple of other thoughts:
- Others have adequately identified that there may be times when a sitter is necessary during general day trips in McKinley, etc.
- Really not a big worry, but how will the dog react to wildlife, not just bears, but wildlife in general? This reaction will either enhance or detract from the occasional wildlife sightings during "RV Camping" trips.
Where the rub comes in is in doing some of the non-typical stuff: Want to go flightseeing? One will have to arrange dog sitting and the flightseeing locations aren't necessarily at the same place as the RV camp; Want to go fishing in a boat? Whether or not the dog can handle it, it will be an additional burden and/or more dog sitting required. Want to go on an ATV trip? Want to go to a museum? Eat out?
There's a long list of activities and having a dog certainly doesn't preclude any of them, but will (to varying degrees) make those activities more difficult. If you will be getting a new pet, I'd suggest doing it after the trip.