Im a woman, i would take down ,better safe than sorry lol
You can also Multitask
1 Hand Drilling
1 Hand Holding up the TV
1 Foot holding the dust bag.
1 Foot Stopping the door from blowing shut.
Practice with the drill on a part of the wall no one will see.
As a guide to how deep, measure up the rawl plug against the drill and go a tiny bit further.
You should be fine