Explosive pushups to increase bench?

Any kind of dynamic effort work will contribute to a lift.  Clapping pushups will assist your benching because it will train explosive movements.  Jump squats will contribute to squats, etc.

If you're on SL you shouldn't be worrying about that kind of stuff yet. Assistance is for when you stop making progress on your main lifts from doing just them.

I think you should do them as your first exercise, or on a separate day from heavy bench presses. I prefer explosive pushups, because there is no deceleration involved. Try to push with as much power as you can muster on each of the 3 reps. The first one should be deep, but for the next 2, stop when you get a 90° angle at your elbows. Don't cheat by flexing and then extending the hips to get higher in the air. Keep your body completely straight. The clapping part is optional, really, what matters is that you really push as explosively as possible. If they bother your wrist, consider landing on elevated surfaces at your sides (some plates will do) for each rep, then resetting for the next.