If I replace the motherboard/logic board will it erase my iCloud?

There is two issues here the iPad’s local storage and what you have on your iCloud account on Apples servers.

Any data that you hadn’t sync’ed up to your iCloud account on your iPad will be lost! Your stuff that is on Apples servers is still safe. You’ll need to log in into your iCloud account from another iOS or macOS device to gain access to it. You will use your Apple ID and the password you setup for it. Apple uses a two-factor authentication Two-factor authentication for Apple ID so make sure you can do it.