Broadcasting Alfalfa seed

This past winter, my alfalfa field received some winter kill. I think due to a warm spell in March, then it froze again. So the field is now half alfalfa and half grass. I generally broadcast fertilizer in the spring in my mainly grass fields. It was suggested to me that I mix some alfalfa seed in with the fertilizer for this field. Do you think the alfalfa seed will germinate, or is it just a waste of money?
Thanks.

Broadcasting Alfalfa seed