I'm assuming you have a PS4 Pro? I don't know how that console works, but as long as it's doing the scaling from 1080p to 4k for you, I don't think you'll have much issue. Sounds like the tvs scalar adds quite a bit of input lag, so if you can do the scaling on the console for a game that's 1080p, you should be fine. Usually those frame interpolation settings add lots of input lag, and black frame insertion can add input lag too.
Yes, I'll be using a PS4Pro.