Two days ago I entered Windows 7 and updates were already downloaded. I am somewhat paranoid, and that bothers me.
I am getting ready to dismantle MS, but until then, someone let me know.
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In such a case the answer is simple NO.
When you start the computer and boot into an Operating System (OS) without using any sort of Virtual Machine (VM), there is no possible way that another OS could run simultaneously.
The CPU will be used by whatever OS you booted into, and no threads/process of another OS that is not running could be processed.
I don't know what else could I say, it is just impossible.
About the updates, Windows is very intrusive. You have to set several configurations to guarantee that no updates are download/installed. But that is not my field :)
Lucio is right that Windows cannot run simultaneously with Ubuntu without the use of a VM.
The most likely scenario is that Windows downloaded the updates last time you ran it.
Windows is much less flexible than Ubuntu (or any other Linux distro) and requires a restart for almost (?) every update. So when you started Windows again for the first time in a while, it was finally able to complete the installation of the updates that it had already retrieved.
Another possibility is that you have Windows configured to automatically download updates, but not to install them without your permission (assuming it prompted you before installing them). In that case 'already downloaded' could mean it happened between the time you booted Windows, and the moment it asked you to install the updates.
If the updates were small it could have happened very quickly.