Thumb Drive Question

[Beartooth]

All of / on my main machine will go easily onto even a 
modest thumb drive -- "df -h /" says only 11 GB; meseems I've 
heard of other people keeping back-ups on thumb drives.

But what about the OS? If I were to put, say, the current 
release of Fedora onto the same stick, would I be able to use 
that, while visiting in-laws for instance, as if it were a live 
CD =with= all my data?