It will probably survive, but it won't be happy about it. Too little sun will cause it to flop. I've grown it successfully in 4 hours a day of morning sun, followed by dappled shade. It does best, however, in 6+ hours.

There are finely bladed varieties of Carex which will do better.

It flops in full sun in my climate! A very wispy, even messy looking grass at the best of times, sun or shade.

I'd agree with going with a species of Carex. Besides not being well-suited to shade, Mexican hairgrass, Nassella tenuissima (formerly Stipa), is considered an invasive species in California. New Zealand hair grass (Carex comans) in one of its green forms can tolerate quite a lot of shade or go with a native species, Carex tumulicola or Berkeley sedge.

Here is a link that might be useful: CA invasive grasses

It self-sows here, too, but not excessively. I let it have its way in one bed, and move the young'uns out to other beds and containers. One plant only looks good for one season for me, so I treat it as an annual, and shovel prune the volunteers before the seed ripens.

It's native to prairies in Texas. Does best with full sun and no supplemental water after it's established. Growth & appearance will be very disappointing under your tree.

thx for all of the suggestions