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.