No. David Crosby was never in "Full House." You must be thinking of Bruce Baum, who bears a resemblance to rock and roll singer David Crosby.
The TV series Full House tells the story of a sports broadcaster later turned morning talk show host Danny Tanner and his three little girls, D.J. (Donna Jo), Stephanie and Michelle Tanner. Before the show begins, Danny Tanner's wife is killed by a drunk driver. So he needs help raising his three little girls. He asks his rock musician brother-in-law, Jesse Katsopolis, and his comedian best friend, Joey Gladstone, to move in with them. As the show goes on, Jesse gets married to Rebecca Donaldson, Danny's co host of the talk show. The two have kids of their own, who are twins, Alexander and Nicholas Katsopolis.
The series starred Bob Saget, John Stamos and Dave Coulier. See full cast and crew at IMDb.
David Crosby on the other hand, is a singer-songwriter and guitarist. He co-founded the pioneering folk-rock band the 'Byrds' in 1964. Later in the decade he teamed with Stephen Stills and Graham Nash to form Crosby, Stills & Nash, with Neil Young joining the group for stretches. Crosby released a successful solo album and recorded with old bandmates throughout the 1970s, but also suffered from drug addiction until being imprisoned in the mid-1980s. He was inducted into the Rock and Roll Hall of Fame twice, for his work with the Byrds and CSN, and later collaborated with son James to create new material.
Complete your David Crosby record collection. Discover David Crosby's full discography at Discogs.