While this will work, as Dan has suggested, it's not a great idea. For one thing you will have no ability to change anything in the application scope on site A without affecting site B. This can introduce head-scratching bugs. Consider DSN names which are often in the application scope. Unless you are using the exact same DSN for both sites, whichever site is first initialized is going to dictate which DSN is used - so you basically have to live with the exact same application scopes.
Still, it can be done. See this post for a plain example that might be helpful.
Application Variables on ICE - ColdFusion Muse