The answer is somewhat simple and somewhat complex.
The basic answer is Yes, you can take it with you.
The complex answer however has to do with Network Television (ABC, NBC, UPN, FOX, and so on)
Where you are you very likely subscribe to your local stations, They are "Spot Beamed" to your general area, For example, I"m in Detroit, MI. The Spot beam includes Detroit, Flint, Mi, Jackson, Mi and flakes out long about Kalamazoo Mi.
So if I'm in Southern Lower Michigan and west of Battle Creek... Odds are it works fine
But if I'm in Chicago, Il, or Dayton, Oh. No joy on watching WXYZ tv.
Exactly how far from home yours will work. I don't know (For one thing I have dish) But that's the problem
Now, if you sign the RV waiver and quite possibly pay a few dollars per month more then you can get one of the "Super Cities" those are on what is called a CONUS beam, What is a CONUS beam? CONtential United States, In short, it works, and it works all over. You still get your local stations if you are close enough to home, but you get the super stations no matter where you are.