The best way to know if your files are still retrievable is to try. On most computers, the permanent storage media is the hard drive that is a separate component from the motherboard. However, Chromebooks are built differently.
Chromebooks have a function where they automatically sync your data and back them up to Google Drive. This function can be turned on/off in the Chromebook’s settings. So, I would first access my Google Drive account and see if the photos aren’t there before undoing all that hard work by replacing the old motherboard.