The box should do a reboot as part of the upgrade. I don't think the GUI will restart. As said above, check the progress log via comand line.
I highly recommend doing the upgrade from the command prompt using the "update download" command to get the bits downloaded. I do this twice to ensure that all the bits are found. the download is a few hundered MB so it could take a long time depending on you network connectivity.. The 2nd time should show downloaded 0 of 0 bytes.
Then I issue the "update install" command. This phase on 8380's takes 10-20 minutes.