You very definitely need to plug the bore with parkerizing.
Not only does it etch the steel, it builds up enough on the surface it could cause high pressure problems when fired.
Bluing usually doesn't require plugging because it has no build up and doesn't damage the steel.
When plugging the bore, you need to take into account the expansion of air in a hot chemical bath.
Normal drive in plugs can be blown out by the pressure, splattering hot corrosive chemicals. People have been badly burned or blinded by this.
This is mostly a problem with big bores where there's enough volume to allow the plugs to blow out, but it can happen in small calibers too.
The plugs need to be hot chemical resistant.
Most professional plugs are plugs joined by a stainless threaded rod and stainless nuts so it can't blow out and you can tighten them in place.
Note also that a "Chrome Moly" barrel is NOT hard chrome lined. Chrome Moly is nothing more than a common carbon steel that's been used for gun barrels since the 1930's. It's nothing special.
These days some sellers are pushing the "Chrome Moly" label to lead the buyer to think he's getting a chrome LINED barrel when he's really getting an ordinary barrel.