Ty,
A couple things about what you're trying to do.
Maintaining an open connection is not expensive for your app, both in terms of battery use and billing. When you issue an HTTP request, it's likely that your HTTP client will also keep that connection open for some time in order to optimize the next request. Requests over HTTP are also going to be less efficient overall compared to the SDK's own persistent connection, which is highly optimized. Going down the path of making an HTTP request for doesn't sound like it would actually help your users at all, and in fact, probably make the user experience a little worse.
Second, user authentication is checked and enforced on the server side, not on the client side. Assuming that your security rules are configured correctly at the Firebase console, no one can really just "create a copy" of your app that chooses to bypass authentication. I wouldn't be too concerned about this sort of thing happening.
Doug