Can people register in the app, then the app would create a User document with their User information?
You can do that if you want to have a document that represents the user. This would help other users to find that user, for example. The CouchChat example does this.
Should that User document contain id/references to other documents that represent meetings?
It's better the other way around, if the dependent documents contain the ID of the user that owns them.
Should I use channels? How can that help me with this solution?
I don't know; you haven't said how you want users to interact. Can users see each others' data?
Should I use persona for an authentication mechanism? What would a user have to do if I used this mechanism. Is authentication necessary?
The client app needs to run a Persona login flow in a WebView to get the auth token to send to the server. We have an iOS library to do this (https://github.com/couchbaselabs/browserid-ios) but not one for Android.