Good Afternoon Richard,
If I remember correctly, the automatic updater runs completely independently of the popups. What I mean by that is the printing mechanism checks the registry every time you send a print job to determine whether or not it should trigger the uniupdater (presuming it exists/is installed). If installed, the uniupdater gets fired up as a completely separate process, and the popup print job continues on its merry little way. I expect you could simply schedule the uniupdater to run at night when the machines are unprotected (if DeepFreeze or other security software is installed). That should result in the machines always being 100% up to date each day. If you are making changes during the middle of the day, there is not much that can be done short of triggering the updater remotely.
In response to the proposal you made above, because the spool file has already been generated (or at least started generating) before the popup client ever appears, any updates made to the packages by the uniupdater would fail to provide any benefit to the job just submitted - even with the rearranged workflow - because at this point in the process it has been already been rendered to the spool file.