I have made 13 round trips to/from Alaska by RVs and about half those rigs had a generator built in. But in Canada or Alaska, I don't ever remember starting any of them. If I boondock, for a couple of nights and run down the house batteries, by driving the next day, my RV engine alternator will have the batteries recharged by noon that day. If your house batteries don't charge off your engine, consider getting a larger cable run between the two.
You generally won't need AC nor lights in the evening, plus even if it gets hot during the day, come evening, just open your windows and turn on your Fantastic Fan or equivalent. Your rig will be cooled off in no time.
On our last 4 round trips to/from Alaska, we had a generator only on one of them since we changed rigs and the current one has a built in, that we seldom use anywhere. If uou have one, a generator, and room for it to go along, then take it, but i sure wouldn't go buy one just for a trip to Alaska or or take up valuable space that could be used for fishing gear.LOL