No - unfortunately they do not have BMDs for Ireland on Ancestry. They have Parish and Probate records for England, Wales, Scotland and Ireland 1500s-1800s but you can bet the lion's share is not Ireland. When you try to search, the only Irish counties available are Antrim, Down and Louth.
If you would like something looking up on that database, post it here and I will check it for you!
7/3