I monitor each and every LIVE feeding until the rodent is dead, and I often see the rodent biting at the paper towel substrate whenever it gets the chance... So I wouldn't count on the rodent finding breathing more advantageous than biting HARD. The rodent will constantly chew at the paper towels until it can't anymore. THEN it will focus on trying to breathe.
I suppose it depends on the size of rat. Like I mentioned before, weanlings and small rats are harmless. I feed smaller and more frequent than larger and less often. It's safer that way. I've never experienced anything you described.