Leaderboard

In theory I think yes, but in practise very hard without seeing the display. One option could be to copy the content of the entire user partition, but again some interaction with the phone might be needed. If you have allowed google to take backup, at the least some data is saved. And if you allowed google to stea...erhm STORE your pictures, they will be saved in the cloud too, maybe in poor resolution though. But start booting it to bootloader. If you see a menu, it is software 'only', so you would know that you are unlikely to need a new display.