I am lucky; in MN a few selected stations have an "off-road" pump delivering non-E gas.
A couple of years ago I dumped the stale mix out of two saws and a string trimmer into my rototiller. It didn't run very good, but it got the work done. I shut down and went in for supper and when I was finishing up later (with a now cooled down motor) I noticed occasional puffs of smoke or steam (it was cool, maybe 45 deg).
That was my impetus to go to the straight non-E gas. The tiller has large enough passages to probably pass some water, and that's where the steam came from. My saws and trimmer probably don't.
Back in my snowmobiling days, it was common to run sleds with no more than a velocity stack on the carb. Of course, the engine could ingest anything that came its way, and occasionally did. The most common was snow. Snow could, and did cause engine damage: snowflakes hitting hot surfaces inside could erupt into steam, steam cleaning those surfaces, and occasionally dislodging carbon on piston tops...a partly dislodged flake of carbon could glow red or even yellow and now you have a semi-diesel with about 40 degrees of ignition advance. Soon after, a hole in your piston.
If a saw carb was to pass pure water, or nearly pure water, I'd expect the same thing.