I'm pretty sure it is possible. I haven't tried but I have successfully installed Mint on a Live USB and then updated it. I don't remember the exact steps, but persisence is required.
You need the extra space to install your updates and programs.
The only problem I suspect is speed. Hopefully you will be using USB 3.0
Otherwise, games and programs will load really slowly in PlayOnLinux and possibly play slow as well.
Let us know if you are able to do it....
I think it would be cool to have a portable gaming Distro on a Flash Drive where you can load up a game on just about any computer.
You may also have problems with proprietary drivers as well. Just depends on which computer you are planning to use.