Apparently so, according to this
website.
Honestly, I usually just use cock/hen with a few select birds such as pheasants (male also called 'rooster'), chickens (male is also called a rooster), guineas, and peafowl - primarily only those which are domesticated or hunted, where gender distinction is more important.
Otherwise, with songbirds and such, I'd tend to just use male/female with most species of birds.
Some birds have specific names for the male genders, although the female name is often just hen or the same as the type of bird it is.
goose: male = gander, female = goose
hawk: male = tiercel, female = hawk
duck: male=drake, femal = duck
turkey: young male = jake, mature male= tom or gobbler, female = hen