Shallow root system similar to a pine. Big Hosta whose roots will grow under the Cherry roots should be fine, Small hosta would probably be choked by the roots.

I guess that is why the hydrangeas have done so well. Can't wait to get started.

I have a garden under a Ranier cherry. I wouldn't recommend it. The roots are very dense. Its difficult to get enough water to them. Most plants stay small.

Here is a S&S after four years of competing with it.

Here is the piece I moved four years ago that doesn't compete with cherry tree roots.

When I dig in that garden it's like cutting through clumps of 20 gauge wire.

This has been my experience. Yours may vary.

Wouldn’t the debris from the tree fall on top of the hosta? I have a maple and a locust which are constantly shedding leaves and twigs. But they also provide the shade for the hostas! Oh well! Hahaha!