Will my big buck teeth remain too long and huge after Invisalign treatment? (Photo)

I have over-jet, huge buck teeth and I'll be getting the Invisalign treatment in two months' time. As you can see, my two front teeth are over-sized and rotated inwards. I worry that even after my teeth are straightened, the over-jet issue will still be there. Is it possible to ask my orthodontist to push my bunny teeth up and into my gums? Will it cause the gums to recede further than it already had, as seen in the pictures? Thank you for your time.