Might not sprout until the spring, but my understanding is the seed will survive the winter. Anything that sprouts this year may get killed off by the first freeze, though.

Not doomed. Not the best time, though, because if/when it comes in you won't have time to evaluate it to see if you need to put down more seed.

Spring is not the best time of year for seeding because that is when the summer weeds, principally crabgrass, is sprouting. Typically the crabgrass sprouts first giving the false impression of success with your new seed. By the time the real seed sprouts the crabgrass is well established. Then, due to the fact that the real grass does not have very strong roots yet, the summer heat can do a bad number on these new guys. The worse news is that crabgrass is a summer annual plant that is designed to grow fast and develop summer roots quickly. If there is good news it is that you can reseed again next fall. For you fall likely starts in very early August when the summer high temps begin to cool off in the evenings. For me in South Texas, our evenings are just now cooling off in the hills north of San Antonio. San Antonio is still hot at night.