Baseball very different because of pitching. Hockey has proven to be the sport where home ice is much less important than home floor in basketball. You really can't compare the situations between sports. To answer the question as far as NBA playoffs go - I don't believe any team has ever lost first 2 at home and won the NBA championship. Some down 3-1 comebacks have occured in different rounds. Teams that have won a best-of-7 playoff series after being down 3-1:
Boston vs. Philadelphia, 1968 Eastern Division Final-x
Los Angeles vs. Phoenix, 1970 Western Division Final
Washington vs. San Antonio, 1979 Eastern Conference Final
Boston vs. Philadelphia, 1981 Eastern Conference Final-x
Houston vs. Phoenix, 1995 Western Conference Semifinals-x
x-won championship
wil.