The only thing I can imagine besides a piece of software that would run the command line softwareupdate on a schedule, you could set the prefs to not automatically download. When updates are available, set a schedule to start your Mac at 3am, shutdown at 8 am, and turn on auto-update just before shutting it down.
Another homebuilt solution may work to create a launchagent that runs at 3am to run,
softwareupdate -d -a
That will download, but not install all pending updates. You can then go into the App Store and install them. Using -i -a would install them if allowed by permissions.
If the LaunchAgent is in the main /Library/LaunchAgents and it should run with admin privileges.
I don't know if it can be run "headless" in the background, so you might have to schedule startups with auto-login enabled.
I don't have my Mac with me, so I can't write/verify that solution.