Yes it works fine -- their policy and this e-mail are explicit that it works "on the go". Your option is a regular subscription.
As long as you pay for a single subscription and you're not sharing it with others who try to keep accessing it after you've moved on to a new location, there's no problem.
Just make sure you log out of your account on the living room TV when you leave a home, that's all you need to do.
That is actually a very good question. I know people who literally do this, though not only moving "households" every few months, but moving countries.
TBH, my guess is NFLX's solution is going to be "Yeah, fuck those 12 people who do that. We've got bigg^H^H^H^H more lucrative problems."
