Does Windows Update download and update in the background even though Updates are turned off?

I have a client trying to run my Access 10 application on a 32bit machine running Win8.1, with 2GB RAM and a 40GB Hard Drive.  (Not joking.)

She claims it is a fairly new machine (which I don't believe).  She claims my application used to work but now doesn't.  It gives insufficient disk space messages.  She removed a printer in the hope that it would save space.  Now she can't re-install it or even copy a small file.

I deleted everything I could, but as fast as I did it, the disk kept filling up until there was absolutely no space left.  My questions:

1. Could Windows Updates be filling the space as it becomes available?

2. Is it possible that 8.1 worked when first installed but subsequent Updates have taken up the remaining space?

Thanks in advance.