No, the only way a member can respond to an App message is through the App itself. The member will receive a push notification to their phone where they can respond to the Message that was sent. The Email/SMS options are useful when some of your members don't have the App downloaded but you want them to receive the message as well.
If you select Email when sending an App message, then a copy of the message will be sent to the member from firstname.lastname@example.org
If you select SMS, then a text message will be sent via the SMS Account your club has. If your club does not have an SMS account, then the SMS will not be sent to the member