With a no see um mesh at the hood, I am guessing ventilation is probably not a concern. I don't think you'd want to open the no see um all the way in a heavy rain, and it would pretty much cancel the insular effects, but it should work. Might not be bad at all to include with the bedroll/swag.

There was one occasion long ago when camping with the family and we had one of those cheap nylon cabin tents. It happened to be a steady rain for a full day at camp, and when we called it a night we zipped it up and stayed nice and dry inside. Meanwhile, the soaked thru fabric of the tent became airtight, and I awoke about 1:00 am struggling for air, as were the rest of the family. I unzipped the door flap and let fresh air and the rain come in. We recovered, although we did get a bit wet.

It can happen.