I think it's possible to make that work, with some caveats.
First, you have to have modest expectations. Maybe you've got a service that you developed for personal use (as in my case) or as a hobby, but you figured it might be useful to other people as well. Maybe you'd be completely content with it making just a couple hundred bucks a month, with no aspirations of making it be anything more than that.
Second, you can't sink a lot of money into advertising your service, at least not at the outset. Which, of course, means you have to come up with more inventive ways to get the word out. Tough, but not impossible.
Third, you've got to primarily target people who understand that for $1 a month, they're not going to get very robust technical support.
And fourth, you're more likely to be able to pull of a $1-a-month price point if you also offer higher price points for premium services. In the case of FAB Apps Bundle, the premium service is targeted to small-business owners and people who manage their organization's Facebook Page.