It'll probably work (if the copy is done right)...I've done plain installs on USB Harddrives (NOT thumbdrives), and moved them from PC to PC with varying hardware configs, without issue (when needing a proprietary video driver such as ATi or nVidia, it might have to be installed, and then reconfigure later when moved off, but other than that...)
Be sure to copy as
root, and get all the permission bits correct (
cp -a, I think?), or better yet, try
rsync (
rsync -a source dest ... read the man page)...
May have to edit
fstab, and re-install
grub, depending on the destination details, but it should work
