If I installed Java (or an older version), will the App Store update my local installation, even though I installed, and updated it outside of that?
Java6 provided by Apple should be updated by the App Store, given any newer versions will be released (which i doubt).
Apple Java RE 1.6.0_51 in a VM. It was updated to
Apple Java RE 1.6.0_65 by
Java7 & Java8 provided by Oracle use their own update services.