Yes, it is possible, but in most cases it's not a good idea. You can certainly use the app and use a lot of things, but -as already mentioned- some frameworks are not present on the Simulator.
One of the notably absent frameworks is the InApp purchases, so if you're targeting that, you won't be able to simulate it (I haven't tried in Xcode 4 tho, but I'm sure it doesn't work).
Also already mentioned are GPS, Accelerometer, Cameras, etc. You can't have those (off the record, as bad as Android 'Simulator' is, you can certainly use some of those in the Android Sim).
Is it recommended? It depends. Nothing will give you better feedback about your app than a real device, however, for certain simple applications, the simulator is definitely more than enough.
Consider (use Google) which features you need for your app, and then take your decision based upon what's available. Don't underestimate the Simulator, but don't try to replace a real device with it because you'll be disappointed.
If you're targeting iPhone and iPad, you'll want to have both, the UI feels (and should) be different.