Tried to hide a dock icon but failed
I suspect that the Clock application is code-signed, which is likely what is causing the crash.  I tried to do the same LSUIElement change in the plist file to Clock.app and it gave the same crash.  Some research told me the following:


  There's one more step to the process if the developer has signed the application with an Apple Developer Certificate — and that includes all Mac App Store applications. Without this step, you'll likely get a crash when opening the app. To prevent this, you'll need to re-sign the application using the following command in the Terminal:
  
  sudo codesign -f -s - /path_to_app/appname.app
  
  Replace "/path_to_app/appname.app" with the path and the application name that you just tweaked the Info.plist for. After doing this, press enter, and enter your password. The application will be re-codesigned and you should be able to launch the app without any issues.


source: http://www.maclife.com/article/columns/easy_mac_hacks_run_os_x_applications_without_their_dock_icon

I have downloaded Clock.app, Added the LSUIElement key to the plist file, and I resigned the application, and it seems to have had the desired result you are looking for.

There are some considerations though, the only way I could close the app without a dock icon was to use Activity Monitor and kill the process.  The link I pasted above also gives a few more warnings you should read before doing this.

Make a backup, try it out, and let me know if you have the same success I did?