Yes, I do that myself. I prefer to save the whole program directory to a USB drive and move it to the other machine. If the machine doesn't support certain aspects, like the resolution, it will go to the lowest setting possible and you can reset it to what you like for that machine. I have a desktop and a laptop. The laptop doesn't support the resolutions or the performance of the desktop, so when I copied it over I had to reset a few things, but it was easy.
Just make sure you never, ever try to sign in to two machines at once, or it will set off alarms at Blizzard, they'll consider your account hacked, force a password reset, and disable the account until you contact their support people. It's a real pain. I was raiding once, and my nephew tried to log into my account on my laptop that he was borrowing. It took three days before I got my access back.