Norcold N300.3 inconsistent propane functionality...

The truck will almost 100% not be able to keep up. But, that might not be a big deal depending on how long you are driving and where the destination is (or more precisely will you have hookups at the destination?). But yes, you can run on propane, they work just fine going down the road. Some will advise turning them off at fuel stations which is probably good advice.