The scarification you get over the tattoo will remove any ink thats there and replace it with a scar, probably the color of your normal skin when it’s completely healed, but sometimes they can stay slightly red depending on your skin type.
If i were you i would let the artist know of your idea and plan that way they can design the tattoo where important parts wont need to be cut out of the tattoo (like needing to cut out the main part of the girl’s face in order for the lines of the cage to be spaced evenly).
But as for how it will look, here’s some examples of scarifications over pre-existing tattoos.
fresh, by Brian Decker
healed , by Brian Decker
healed, by Thorsten Sekira
heart scarification healed a little over 5 months, by Anders Allinger
I hope this helps!