Don't focus on people who aren't your customers, focus on people who are.
Totally ignore pirates. It's a waste of your time.
The problem is the server resources they consume. If I just ignore the pirates and the legit/pirate users ratio continues to be the same, I'll need 5x more server capacity to keep the app running. That's a really big increase in the hosting costs.
I wouldn't disable it totally, they will just move to giving prominence to something else. Just throttle the amount of bandwidth pirated accounts consume. They are likely giving you sales you wouldn't have otherwise.
But if most of the people the pirates show that app to are pirates, those network effects aren't in his favor.
I seriously doubt the buyer/pirate ratio is going to stay constant or increase with increased pirate views. Why would it?
When I was younger, I would pirate the hell out of anything and everything. I would only buy it if it was too difficult to actually find/crack. Many pirates will just give up (and not pay either way). But, I think a larger percentage of people that would actually buy it (compared to the number of pirates that will pay a dollar out of the kindness of their hearts).