Well, just throwing random files into an Xcode project isn't really the way to go, regardless of the language. AppleScriptObjC can be used in an Objective-C project, you just need to set things up to load the files and give Objective-C information about them so that they can be used:
- The AppleScriptObjC framework needs to be added to your project;
- An informal protocol needs to be set up to declare the handlers/methods in your scripts, since AppleScriptObjC doesn't have any headers;
- You need to add statements to the main.m file to load the AppleScriptObjC scripts;
- The script classes need to be instantiated in the Interface Builder or manually in your startup code.
I blew the dust off an older example project of mine that uses a couple of AppleScriptObjC files (they don't do much, mostly logs and a Finder window) from an Objective-C project - it can be downloaded here.