Yes it should still work. If you change the assembly to one that isn’t original to that iPhone X everything except the FaceID should still work - I have done so several times for clients. So the reason for yours not working is probably the same small scratches and cuts you have seen. The cable is a bit fragile and some of the copper leads running through it are extremely thin.
I find it better, regardless of if your new screen comes with the transparent front camera frame, to remove the front sensor assembly from the old screen with the frame, and lifting up the whole assembly using the frame. That way you do not need to apply heat directly to the fragile assembly, but apply it to the other side, the front of the screen at the top, instead, to soften the frame adhesive. The frame is then usually easy to pry loose using a narrow spudger, and comes off cleanly. After that it is much easier to remove the sensors and microphone from the frame, no heat needed usually. And if your new screen doesn’t come with the frame, just plonk the whole frame/sensor assembly down in the right place, and boom, Bob’s your uncle.
What's the deal with these particular screws? I have found them much much harder to remove than the equivalent screws on any previous iPhone model. Am not sure if it's the head groove shape or if they are just secured very tightly. More than once I have ended up completely ruining the head grooves without getting them out. Any tips?
What is the reason for the recommended practice of plugging it into a power source on first boot after reassembly?