Yes.
The easiest way to monetize is with banner ads from one of the 40+ authorized Facebook ad networks. http://developers.facebook.com/adproviders/ Believe it or not, people DO click on banner ads, and you should see about a $0.10 eCPM for US and UK traffic. (Traffic outside of those two regions often have less than a penny eCPMs.)
The second-easiest way to monetize is to create a virtual currency that has value to your users, and sell that currency via Facebook Credits. http://developers.facebook.com/credits/
I've personally built about a dozen Facebook apps, and have been involved in close to 100. A general rule of thumb is to expect to make $100/month for every 10,000 monthly active users (MAUs). A modest success on Facebook can garner about 100K MAUs which should net you in the low thousands of $USD per month.
If you want to support yourself full-time, you'll need to aim for 1,000,000 MAUs.
Hope this helps, and good luck.