Not only can infants be signed up for FF programs, they can earn elite status cheaply. If you call the airline to make their reservation, or use expedia.com you can frequently get a child's ticket for 1/2 price or less, with full FF miles. My youngest son, now age 2, was confused about the small seat (his FAA approved booster seat did not fit in the coach seat.) and limited service on a flight when, for the first time in his life, we did not get upgrades on a segment. (note: We did have to use milage upgrades for him until he became elite and started earning his own upgrades). He was 10 days old on his first flight. Before he turned two, we usually bought him a seat on any trip over two hours.