My guess is that if the TV antenna is completely powered down (including power to the built-in amplifier), interference is unlikely, except for line-of-sight issues. I.e., if the TV antenna (or anything else metallic or dense) is between your other antenna and its signal source, there may be issues.
Formerly: 2005 Airstream Interstate (Sprinter 2500 T1N)
Now!: 2014 Great West Vans Legend SE (Sprinter 3500 NCV3 I4)