What are the implications of linking your Apple ID to your Mac User Account in OS X System Preferences?
After associating and Apple ID with you user account you'll be able to use it to:
- Reset your login password (unless FileVault is enabled)
- Establish file and screen sharing access to the computer from another computer
- Share files and screens with another computer after you log in
And for the particular case you mention regarding the Mac App Store, no, associating an Apple ID with a user account won't change the Store's password prompting.