Looks like you can do this via the Terminal - I tried this on a 2012 Mac mini with the 10.10.4 updates. It almost, but not quite, worked:
sudo softwareupdate --list
sudo softwareupdate --install -a
However, at this point my ARD connection died. I couldn't reconnect. Fortunately I'm in the same building as the server, so I walked downstairs to see that the terminal was displaying:
software updates have been installed, please restart immediately
A this point, I entered the command:
sudo fdesetup authrestart
from the physical keyboard, and it rebooted and did the updates.
I wonder, in the 2nd step, when the ARD connection was lost, could I have run another terminal command to get it back online so I could issue the final fdesetup authrestart command?