If you overseeded winter rye grass then yes!
Every winter I talk to people that have moved here from another state and can not figure out why their grass is "dead". Most Arizona homes have bermuda grass. Bermuda grass goes dormant for the winter and turns a light brown. The good news is that once we warm up again with high 80's or low 90's temperatures the bermuda grass becomes active again with a little water and will green back up.
Winter grass does need to be overseeded every winter. The ideal time to install winter grass is the month of October as the germination is dependent on the evening temperatures. Using a perennial seed instead of annual will produce a thicker, greener grass. With the correct watering schedule, seed, and some manure topping you will have a lovely winter lawn within approximately 14-16 days.
If you are in the east valley and looking to sell your home I offer free landscape services so that you can take care of the inside while we handle the outside.
For buyers we offer landscaping changes at cost for a period time after you move into your new home.
Your AZ Full Time Realtor offering Curb Appeal.