No, local channels like; ABC, CBS, FOX, NBC, Telemundo, etc. are based on where you are when you stream FuboTV.
If you travel away from home, you will receive the local stations that are available where you currently are.
What about my Regional Sports Networks?
While regional sports networks will travel with you, any devices you have used outside your home area must have been logged in to the FuboTV app from your home area at least once in the last month in order to keep watching while away from home.