I'll assume that it's best to put in the check after you've found a bug. Perhaps something that the monkey triggers that isn't very high on your human-customer buglist.

I'd imagine there are occasional uses for it. You could use it to start the app with a particular state you wish to test with Monkey, while leaving it usable for human users.

Maybe. Sometimes no matter how hard you try test and production are significantly different. I wind up in a number of situations where any meaningful testing has to be done in production.

You might avoid doing certain write-esque operations if you know you are in test mode. For example, you wouldn't want to charge a credit card or update someone's facebook status.

The intended use for the Mac equivalent (described in the folklore.org story linked from another comment here) was to disable the quit command, so the test could be run for longer than it took the "monkey" to quit the application.

I imagine there are similar uses on Android.

It's meant to test some of the more extreme bounds of the system. Filling the event queue faster than the code can handle it, for example. Clicking in odd places at strange times and seeing unexpected behavior.

Monkey testing is going to expose things that you never anticipated in your test spec. It's a stress test.