Yes, and No….
OEM, original screens for the iPhone 5s CAN be used on the iPhone SE. However, the most recent iPhone 5s screen designs being produced by Chinese off-brand producers are no longer compatible with the iPhone SE. You will have to purchase a iPhone SE screen, which runs a few dollars more than the iPhone 5s screen.
There are workarounds according to a few sources, but the reward is definitely not worth the time and effort.