The quick answer is Yes and No.
No, because you cannot directly promote an app profitably at the moment. Not at the cost per click rates that you get on Facebook today. The lowest you can hope to pay for most demographics is about 0.40cents. To promote a $1.99 app, you will need to get about 1 download in 5 to break even., that is a 20% conversion rate!
How to promote an app strategically on Facebook
The best way to promote on Facebook is to send the traffic to a Facebook page. When users like a Facebook page, you can then continue to market to them for free.
It is not as straightforward as I make it sound but such is the nature of the App store. You need a solid business strategy here, no time for hobbyists.
Anyway, back to the Facebook tactic. Ideally your app should have a target audience. Let’s use “New Moms” as an example. Your Facebook page should not promote your app directly.
It should talk about topics that binds “New Moms” together. Facebook is a social network, and things need to be social for any strategy to work.
Check out this Facebook page, Being Mommy. At first glance it doesn’t look like it promotes any product right? Wrong, they have a community of moms that the owners engage in conversation about things that are dear to their heart.
Now that they have the attention of these moms, they can now insert information about apps that are relevant to them.
Normally you wouldn’t do this for just one app, you may start with one app but if you as smart, you will make apps that tend to the same demographic. This way, you will spend even less and less on marketing because you have that audience.