Can I switch my battery & screen without switching the motherboard?

Switching the display and battery over shouldn’t give you any issues with overall functionality, but you will probably get some notifications about the phone’s ability to verify a genuine display or battery is installed. Even though they may be genuine Apple parts, Apple pairs these components to the board with their serial numbers so putting different parts in triggers a mismatch warning. As long as you don’t mind the notifications, then functionality should be mostly intact.

You’ll want to make sure you also swap over the front facing sensor assembly to the replacement display since Face ID components are also paired to the board and without the original components, Face ID won’t work. Realistically the only downfall would be the lack of True Tone, which can be transferred via one of the many programmers available if you want to go that route. In my opinion, it’s a pretty minor inconvenience to go without.