Too drunk to go back and look for your original post, but if the meat of it is that you’re going to shut off your water once the thaw hits, yes, turn your water heaters to pilot mode. My mom had her water cut off (by the city) and her water heaters were making gurgling/strange noises during that time that they were not receiving water pressure. I’m not a plumber, just have general knowledge, but that tells me that the heaters were boiling the small amount of water left in them. While that possibly may not have detrimental effects, it’s easy enough to shut off the heaters for a bit, just in case. It certainly won’t hurt, especially after we get back above freezing.
Ended up scrolling back to look for your original post... again, drunk and have nothing better to do. Even if you’re wanting to shut off the main before the thaw hits, I’d definitely shut off the water heater when you shut off the main. With no water moving through pipes/faucets, it won’t benefit you to have heated water, so may as well shut it off and not risk overheating the water heater (as long as it’s insulated or in a warmed area).