i know some linux distros will do this, they're called live distros. or maybe you just boot from a flash drive i don't remember. the problem with this would be having drivers for all the possible hardware that you would use this usb flash drive os with. that would be a pita to make it work.
i think when you install software it puts registry files in you os disk, so unless you carry around you hdd along with you usb drive, you would have to install the software on every hdd in every pc you use.
The answser to that would be NO. USB is a lot slower than the read/write speed of a hard drive.