I'm actually slightly worried about that, since I don't know what happens when I, a PC master race demigod, play with a degenerate console peasant. Is input lag a contagious disease? Is it airborne? Does it travel through ethernet cables? Should I wear a mask? Gloves? This is unprecedented, except for all the precedent it has, but I'm ignoring that because it doesn't support my stance!
Kind of don't think so, but it also could be dependent on what is causing the lag and I've never been clear on why consoles so consistently have such comparatively high input latency.
There is the V-Sync conversation, but that's not console specific, doesn't explain why it varies per console, why it's several frames, and (to a lesser degree) how some games (Tekken) improved things with software changes.
You are most likely to deal with an uptick in WiFi percentages, and base PS4 players stalling frames (which I assume is still happening). You've likely run into a few PC players where their systems couldn't pace at 60fps, so likely a mild form of that experience.
With V-Sync forced, on and likely mostly 60hrz TV's, PS4s are probably going to have more drag on the game's internal pacing than a properly set up PC would. That stuff translates into wait states to realign the frame you are supposed to both be playing on. Drag on the game clock has tended to be the thing that causes better systems to pay the higher price in a rollback game, though I think GGS handles that about as good as anything out there ever has.
There is a lot going on though. Like why did PS5 have the worst input latency when it was the fastest of the PS consoles? Just have to see how it plays out. So far it's what, Power Rangers, KI, and SFV with PC crossplay? I don't know anything about PR, and SFV's probably doesn't count as a real example of what to expect. KI was quite a while back, but probably the best example given they have similar netcode success stories and expertise.