Yes — ScoreCam automatically backs up your settings to iCloud each time the app goes to the background. If you delete and reinstall ScoreCam, your settings are restored from iCloud on the very first launch.
What is restored: All app preferences (team names, colors, scoreboard profiles, highlight settings, video format, and all other settings), plus the five data libraries (Scoreboard Profiles, Team Library, Game Type, Description, and Score Type). Logo and branding images are not included because iCloud’s key-value storage limit is too small for binary files.
To verify it is enabled: iOS Settings → ScoreCam → Support → Restore Settings After Reinstall should be toggled ON (it is on by default).
To start fresh on reinstall: Turn this toggle OFF before deleting the app. When turned off, the existing iCloud backup is removed immediately, so a subsequent reinstall will start with default settings.