Hi,
Thanks for your question. Yes, Animation Module will trigger off of the Ballista entering the battlefield, and the Orb won't stop it. The Ballista entering the battlefield isn't the relevant part here. It's that, because of 122.6, entering the battlefield with a counter counts as putting a counter on that object. Putting the counter on as it enters is what the Module is triggering off of, not the Ballista entering, so the Orb won't prevent the Module's ability from triggering.
122.6. Some spells and abilities refer to counters being put on an object. This refers to putting counters on that object while it’s on the battlefield and also to an object that’s given counters as it enters the battlefield.
Thanks,
Nathan Long
Magic Rules NetRep