Hope I'm not getting off the subject by asking this? "But here goes", With our CTD's can we stop and filler-up with fuel,leaving it running and not cause it to throw some sort of "Code" by taking the fuel cap off with the engine running??
The CTDs do not have the emissions equipment that a gasser has... the emissions equipment is what causes the code to pop when the gas cap is left off...
So to answer your question, no they will not throw a code if you fuel while the truck is running.