Does the App Store update Java, if installed?
Java6 provided by Apple should be updated by the App Store, given any newer versions will be released (which i doubt).

(Tested with Mavericks &amp; Apple Java RE 1.6.0_51 in a VM. It was updated to Apple Java RE 1.6.0_65 by App Store)

Java7 &amp; Java8 provided by Oracle use their own update services.