It is possible. Here is a list of applications currently using it, their schemes and a link to the info on getting your URL registered.
As a note, these schemes only work on the iPhone/iPad. You will want to make sure only iOS users see the page with the URL (if it is universal, or if it isn't, only iPhone users) or the users may get confused/frustrated that it is not working properly.
I thought the original poster wanted to download and run an app from a web page.
It is possible to use custom URL schemes, but they are not regulated or controlled by Apple in any way. Anyone is free to pick their a URL scheme, including the one you just picked. That would be a mess.
The user will still have to download the app from the App Store. It would be better if the app maintained its own list of URLs to load data from.
True and although native applications cannot be downloaded and run from a webpage, HTML5 web apps can. They feel native, and look great. There were several Google Voice HTML5 web apps before Apple approved the native apps... They looked like a normal app, felt like a normal app, but were 100% web based. It's actually the way Apple tried to go originally with the iPhone...