Oh, it will... but if you log on from a PC, or from an Ex-Box, you'll not have access to any of your account features, including any stuff you bought from the Atom Shop. Which kind of ticks me off, 'cause Bethesda damn well ought to know what I spent money on, so there's no excuse for not letting me have that stuff across different platforms.
To clarify, what is meant by "different platforms" is different OSes. If you move from one PS4 to another, or from one Ex-Box to another, you're not changing platforms, and your account, characters, and purchases should all be there.
I am not certain, but I believe that if you go from PS4 to PS5, you will also still have the same account features available.