Good question.
I'm not sure. With the current version it might because it writes to the core/cache directory. It writes there in the Manager, and reads there afterwards from the UGM script. Of course the new core files also get copied to the core directory. UGM also creates a temporary directory and writes to it, but I can't remember if it's in the core or not.
If you have time to try it, let me know. Delete the core/cache/upgrademodx/versionlist file before testing to make sure it's not just using the old copy. For testing purposes, you can set back the settings_version System Setting to an earlier version (it doesn't have to be a real version) and "upgrade" to the current version.
I wouldn't do it on a production site, though.