Yes to the generator, no to the noisy part. You can run a generator but you’re not meant to be disturbing the area in a number of ways, including through noise.  I would imagine if the generator noise was a consistent issue, and enough people had complained, something would have been said to the leaseholder. Assuming that the cottages on Cauchon are leases and not actual carve outs of private property, I think there are/were a few of those on Cedar if I’m remembering correctly.