250.54 actually says this.
My take is that it can't be an auxiliary grounding electrode unless it is a grounding electrode as specified in 250.52. The only requirements you get a pass on are the bonding and resistance requirements as noted.
So, for instance, I don't see how a 6 foot rod would qualify as an auxiliary grounding electrode.
Having said that, I don't recall any provision of the code that bans bonding of a piece of metal that is stuck in the ground that is not either a grounding electrode or an auxiliary grounding electrode.
ETA: I think all this provision does is allow you to install what would otherwise be a grounding electrode and not have to bond it to the other grounding electrodes by calling it an auxiliary electrode.