All conversions between logical and device spaces are done with the painters matrix.
Usually you don't need to alter the device space. You want to make drawing easier for you so you alter the user space in a way that is more convenient to your purpose.

Is it possible (or better yet advisable?) to define a viewport that is larger than the device I'm painting on?
Yes, it is possible to do that. The mapping to device space will be done with a scale matrix.
I don't know about advisable. What's wrong with an 1:1 scale? Is the output device too big?

Is it possible (or better yet advisable?) to define a viewport that is positioned outside of the device I'm painting on?
Well, what would that solve?

Have you read this:http://doc.trolltech.com/4.3/coordsys.html? Especially the Window-Viewport conversion section.

Regards