Update preferences are set in the preferences window and it's possible to turn them off altogether, download only, or download and install. I believe the program checks at launch by default, provided the Internet connection is active and not firewalled to block Adobe Reader.
You can simply "push" the updates (from what I've read) using an API that installs with admin rights from the initiation point. I'm not a network administrator, so I have no expertise in this area and I may be 100% wrong.
Otherwise, someone with "limited" user rights is prohibited by Windows from installing software. That's not an Adobe setting. Since most any software requires admin rights, this is an uphill battle to fight.