I don't think so.
We went last year during Father's Day, and there were no special activities. I e-mailed Disney to check, and they just recommended activities which are available all (or almost all) the time: golfing, fishing, Richard Petty driving, etc.
We ate at Whispering Canyon and thought they might do something special, but they didn't.
We'll be there on Father's Day, again, this year.
Since they have special activities for Mother's Day, I wish they would do something for Fathers, too.