You can play Force Choke on your own units. You can play Force Choke on Vader. Both instances trigger his direct damage Reaction.
However, if the Force Choke kills Vader, I don't think you're getting the direct damage, as the Reaction only kicks in after the triggering condition (the Force Choke) fully resolves, which in my example would kill Vader and have his card sent to the discard pile where it does nothing.
As long as you're fully aware of the Action window diagram in the rulebook, tricks like this make for great plays. I've often Force Choked my own characters to trigger this as a work around to get rid of Vehicles with 1 Health (or with 1 Health remaining) that are camped out on the other side of the board.
It works really well as a way to bait out C-3P0 from your opponent, if you want to make sure you can get that Force Lightning or Superlaser off without that droid jumping on it. Choke your own guy out, put the damage on Threepio, unless they discard Threepio to cancel it, which would actually help you because they would discard Threepio, you lose Force Choke to the cancel, BUT your unit you were planning to kill survives, so you're better off.