It can be a problem, and more or less likely depending on where your rig is parked when not in use. In a barn, on a farm, tall grass, etc adds greatly to the possibility of critters, especially rodents. Some owners would say that using a rig cover encourages critters to take up residence...
As indicated, you can buy screens for the furnace exhaust areas and also for the water heater. Look underneath and plug any obvious access holes. Don't leave power cord or hose running down to the ground where critters can use it as a bridge, etc. Don't leave anything in the rig (food, etc) when it is not in use that might attract critters.
We use mothballs in the refrigerator and WH compartments, but still got a spider web in the WH burner tube last year. Some people hang an owl on the top of the ladder to discourage rooftop pests. I check the rig frequently, looking into the engine compartment and similar areas for nests, etc.
Paul (KE5LXU) ...was fulltimin', now parttimin'
'03 Winnebago UA 40e / '05 Honda Odyssey toad