Is there a way that I can store the Android app online, and simply load the webpages in a WebView, and have it work? I really just want to expose the Titanium APIs to the WebView, and be on my way, but it seems that Titanium may be a little more restrictive than that.
Titanium cannot be exposed through a remote WebView. You could download code and inject it into a local webview, but it's not recommended. It's better for your users if they can use your application without requiring a network connection and/or have to download the page every time.