No, Twitter's documentation for new direct messages here says that the api:
Sends a new direct message to the specified user from the authenticating user
so the app must send the direct message from a user and not from the app (the info box on the right of the docs says "requires user context").
The only way to make your app appear as sender would be to create a Twitter account with the app name but the user that receives this message would have to follow your app first to be able to receive the message.