For the purpose of slinging the rifle over your shoulder, but shooting with the sling hanging loose, this should not affect anything. As JJ said, if you use a "loop" or "Hasty" support sling, it could remotely affect POI.
But then again, the USMC teaches (or at least did) to use a loop sling for M16 and M4 qualification out to 500 yards. Those slings were about as taught as you can get without cutting off blood to your arm, and they were attached to the sling swivel hanging from the gas block of the M16. The gas block attached to the barrel, so same concept. I never observed a significant difference from using a loop sling to just firing from a rest. With this in mind, I say that it will make no difference as long as we're not talking about a pencil-thin barrel. It does not appear to be.