Will it work?!?

Yes, it does.

See, the "diode" component itself, the semiconducting tiny little crystal, has two polarities, positive and negative.

It just happens to be mounted in a metal case. It's not connected to it but the metal case conducts electricity. The diode is pressed in a module, module is set-screwed into heatsink, heatsink is secured in the host.

So essentially, soldering a wire has exactly the same effect as welding that wire to the aluminium host - obtaining the battery side which is not facing the driver and module assembly (you NEED to obtain that side, which is negative in our case, and get it to driver negative input).

You need both driver inputs and both driver output to have a complete circuit.

Then back to the question, if the unused pin is not needed to complete the circuit is it ok to trim it and forget about it?

sure is, but people (including myself) leave it just incase they need it for whatever reason.