Only if they had been synced somewhere, maybe iCloud, Photo Stream? That screenshot is Recovery Mode. While you probably don't want to hear it, this is why you back up the device regularly, especially if there is content on it that you do not want to lose. Take the time now to set up regular backup, either with iCloud or iTunes and follow that. You can backup daily with iCloud by connecting the device to power and Wi-Fi, it will do it automatically. About backups in iCloud and iTunes - Apple Support
That requires no other intervention by you after the initial setup.