Can I unlock operators on PS4 from owning PC version?

I currently own CoD: MW On PC (Battle net) but was unable to play it.
I have now downloaded warzone on PS4 but I don't have all operators since I don't own PS4 CoD: MW.
Both are linked to the same activision ID, but I have never actually logged in to the PC version yet.
Does anyone know if the operators unlocking carrys over?
My best theory would be I would need to login to PC and load up warzone at least once for it to "unlock" them, but was unsure if it would be worth attempting.