You won't really be able to let the weight drop fast enough to do that on a smith machine. Plus even if you did how is this really any different than doing regular speed benches against doubled mini / monster mini bands. I'm assuming you do use bands to speed bench?
Maybe try free squats against bands, triples have worked well for me. If you're used to doing "the standard" 2 reps this will be way different for you and have direct carryover as opposed to box jumps.
You can only train the muscle you have to be "x" percent efficient. If everyone could get faster and faster, everyone would run like Hussain Bolt right?, or whatever his name is... IOf you think you've reached your speed threshhold, swith it up to a RE day and do speed work on your deload weeks. Ive done that before with success. Good luck Fletch