As Quinn & others have indicated, the Mac App Store rules do not allow a scripting program to directly target any built-in application that has overly-broad access (including Finder, System Events, Terminal, etc.).
However, there is still hope, if not for a 'pure' AppleScript app then at least on the Cocoa / AppleScriptObjC side ... If the latter approach is indeed desirable / feasible, then note that OS X 10.8 introduced the interesting NSUserScriptTask class-family, which does allow running various types of scripts that target arbitrary applications, in a Sandboxed environment. Such scripts must be located within a special 'blessed' user folder; more specifically, your program's designated sub-folder within it, denoted by the 'NSApplicationScriptsDirectory' constant (which currently resolves to: ~/Library/Application Scripts/<your app's bundle-identifier>).
Your Cocoa / ASOC program does not have write access to that sub-folder, so in the typical scenario the user would [agree to] manually place scripts there. The key is that the user, not your program, remains in control of access to such 'blessed' scripts, including any of yours that s/he may install there. Since the scripts could be removed at any time, your program must also gracefully handle their absence (e.g., by re-prompting to install).
If your program also needs to obtain the results from such scripts, rather than just running them, then the various 'NSUser{AppleScript | Automator | Unix}Task' subclasses are tailored to do so respectively for AppleScript, Automator & Shell scripts.
From this perspective, for instance the NSUserAppleScriptTask subclass could be considered as the Sandbox-compliant edition of the older NSAppleScript class. There is one important behavioural change to remember, though; viz., NSUserAppleScriptTask's '- executeWithCompletionHandler:' method executes its associated AS script in asynchronous mode (which is why it uses a completion handler-block), so if you need to emulate synchronous execution instead then just use an appropriate thread-synchro mechanism (a lock, etc.).
[BTW, not really sure whether I'm allowed to say this in the forum, but there is a useful article on Sandbox-compliant scripting available at the 'www.objc.io' website: 'Scripting from a Sandbox' (Issue 14: Back to the Mac, July 2014).]
Best of luck,
--Paul