do not do this please. if you have a good product, people will pay for it. if you don’t, you don’t. don’t optimize for free-loaders
Plenty of apps do this - looking at the first browser tab I have open I see gmail which does exactly this.
For a pure client app like an iphone app, you don't have any real "per user" costs, so there are no concerns about going under from the costs of attempting this. It would be very different if you had to pay for server capacity.