Can one Animal Crossing New Horizons digital copy be used on two Switches with two islands?

I have two switches. I am happy to configure one as primary and the other as secondary under the same Nintendo Account.

I have one copy of Animal Crossing: New Horizons, which is a digital download. My understanding is it can be [shared across two consoles](https://en-americas-support.nintendo.com/app/answers/detail/a_id/47524/%7E/how-to-play-your-games-across-multiple-systems).

But when I do so, do I get a separate island on each console?