If I keep feeding my birds throughout the fall, will it stop them from migrating?

It's an "old wives tale" that keeping your feeder filled year 'round may somehow stop birds from migrating!

Ornithologists who have studied bird behavior and “artificial feeding” determined long ago that plentiful food at a feeder will not change the timing or act of migration. Quite the contrary, “tanking up” at a welcoming feeder before or during their journey can actually help migrating birds.  A ready source of food allows birds to get their fill without expending as much energy searching for it.  Resident species will appreciate a continued supply of seed as well, since colder months place an additional hardship.