Provided you keep a clean galley free of food other than what's in the fridge and nothing particularly odorous, and a clean campsite, I personally would feel safe leaving it in a locked galley. A determined bear won't care if it's in the galley or your trunk...they'll get in. If it's a patrolled camp area, I'd ask the ranger for a local opinion. If you're somewhere like Yellowstone where there are many other campers likely not as diligent, the bear will move on. The opposite could be true as well...depends on your trip and time of year.
I have a Snomaster fridge that I leave on in the car 24/7 over multiple week trips with no issues, some days only using the car for 30 minutes or less. It draws about 2.5a/hr and I notice no impact on my ability to start the car. I follow a lot of people that use dometic's in their Jeeps/4Runners with no issue either, though occasionally hear of dead batteries. Often because the battery was near the end of it's life more than the fridge being the primary cause. Nice thing about it being in your car is food/beverage is always with you when you leave base camp behind. We liked being able to run into town to buy food and putting it directly in the fridge. We now keep all food/fridge in the car. I'd recommend testing that before your trip...run it for 12 hours overnight, or whatever you think will make a good compare to your trip.