My brother was a named driver for his first car (Nissan Micra 1.4 SE+ which is now sold), it definitely made it cheaper.
About the box fitted to the car, my instructor was telling me it can be cheaper but if I was to drive after 000 - 0500* I could get a fine, there are also other limitations.
- Whilst this shouldn't affect me too much, it is possible I will be doing some very early starts - mostly for when I do the on-site part of the apprenticeship for a few months.