It should grow fine. Look for one that becomes dense (spreads fast), and has slow growing seed heads and flowers. Most varieties are very thin and weedy looking. Most varieties send up a flower or seed stem that grows much faster than the rest of the plant. There used to be a variety available called Techturf or Turffalo. The flowers and seed stalks grew at about the same speed as the grass itself, so it was less weedy looking. Plus that stuff spread like wildfire in the full sun. Unfortunately it never caught on, prices remained high, and it is now out of production. I believe there's one called UC Verde that would work although it might only be available in California.

See if you can find some growing at a local garden nursery. Wipe your arms across the surface of the grass and go look at some plants for 10-20 minutes. If your arms get so itchy that you claw yourself bloody, then you are allergic to it and should avoid it in your yard.

I hadn't thought about allergies. Good point.

Would it stay green for all or most of the year here?

Very likely to stay green in a warm winter. If you can find it in a nursery, ask them to direct you to installations they have done so you can see it in action.

Thank you!