Is this the same as line in the sand?

[wobster]

myself, I would have dumped her, but I haven't had to eject a single person in 4 years of plate and 2 years of pitching machine.

Here is a pretty simple question......when you eject a batter does that count as an out as well? I don't have a rule book with me and I am curious since I have not had to call it.