Can I build an application using AppleScript?

Yes! You can save your script as application and create standalone applets and droplets (which will process files/folders dropped onto it).

If you need an interface and are using OS X with a version at least 10.1.2 you can explore AppleScript Studio. This is a robust AppleScript driven front end for building Cocoa applications. It is available as a free download as part of the Developer Tools.

You can also take a look to FaceSpan, which has released his first OS X version of this tool.

You can also use Smile and its dialogs (similar to Studio and FaceSpan, less powerful, but easy and faster developing and debugging).

In OS 9, two products can give your script an interface, allowing you to incorporate text boxes, pull down menus, radio buttons, and more. FaceSpan is a full-featured interface builder that sells for $199. You should also explore the Dialog Director scripting addition.