This is a bad idea for more than one reason:
1. The TV will be a distraction, and reloading is a task that demands your full attention. You earlier raised concerns about double charging cases, and distractions are how that happens.
2. Priming compound is lead styphnate. This means that every time you fire a gun, you're atomizing lead. As such, fired cases are covered in a residue of lead. Dry tumbler media, therefore, is essentially lead-rich dust, and some of that lead-rich dust stays with the cases when you pull them out of the tumbler. If you set up your loading bench in the family room, you create a significant risk of contaminating your living area.