I am a Cerakote applicator (amongst other coatings like Duracoat) and I can tell you that if the parkerizing is not brand new with no oils on it whatsoever you can overcoat in Cerakote or Duracoat.
However, if the firearm has been parkerized for a while and has had its dowsing of oils, etc. I as a professional service would not take the chance.
The porosity of parkerizing really holds the oils to the metal quite well.
I suggest a complete dismantle, a major de-grease with a cleaning solvent, and a final bath in acetone, then a abrasive blast with aluminum oxide in 1200 mesh. I would then do another wash down in acetone, then heat the items up with a hair dryer to pull out any moisture. Allow them to cool down to room temp, then apply your coating.
Long term coating success on a firearm has a lot to do with appropriate and complete preparation.
I offer the above free of charge, with no warranties expressed or implied