The RPG round itself with rocket motor and warhead with sundry ignition devices etc is indoubtedly a dangerous thing to be carrying around and an explosive, and certainly against the rules to just carry on an airliner, at least in the U.S.
There are some provisions for exceptions to allow "minor league" explosives such as small calibre conventional ammunition, pyrotechnics, etc in small quantities to be carried, but those are very special situations with military, etc and you don't even want to know who must approve the exceptions.
As far as carrying on an airliner in the U.S. the empty launcher would probably be looked at very carefully and likely would be confiscated the same way an hidden, unloaded firearm would be.
Previous post was a little flippant, forgot everyone had their sense of humor safety wired off on or about 9/11/01