Remastersys will master your system as you have it. The drivers are on
an installation disk and that is what you get with a thumb drive is the
USB equivalent of a disk. Non-free drivers (propriatary drivers) need
to be downloaded so I don't know if your question has an answer.

Go to Full Circle Magazine, download issue 45, look at page 13 for an article on
Multisystem. It can create a "persistent" flash drive, so when you download
things they stay downloaded. I used it to create a flash drive for testing
Natty, and it's working just fine. I've installed a video driver and numerous
programs, changed the wallpaper, etc.

It can also load multiple OSes on a single (large) flash drive, but I'm not
using it for that.