Would cork flooring underlayment help with vibration dampening in a sub floor?
I don't have any experience to say for sure one way or the other (except that I've not had any notable vibration problems with my front load HE washer on the first floor, which is just sheet vinyl on 3/4" plywood, near the end of the joists). But what I'd think you want is basically the same thing that that you want when you're soundproofing a floor; you don't want vibrations at the top to transmit elsewhere.

When soundproofing, what you really want is a sandwich of plywood, underlayment, plywood. So roughly what you're suggesting. Cork can work well, though rubber underlayments generally perform much better at the same thickness. You lose a lot of the benefit if you screw the top layer to the lower layer, though - you want the layers glued together, without anything hard bridging across the soft layer.