Yeah, that would be pretty cool. Our organization certainly put a lot of value on having analytics for the app, and I suspect many others feel the same. Filtering the logs for webservice calls isn't quite enough. If you get to it after you guys upgrade Ionic versions, you could use the extra Ionic 2 plugin, which would be helpful.
One thing that would be interesting to explore would be unifying analytics across Moodle Mobile and Moodle web, using the GA setID function to track users by their moodle ID (GA would, of course, anonymize this). So you could follow users as they moved between the app and the website. But I've heard that if you give a website and a mobile app the same GA property (tracking code), some stuff can get messed up. And if you want to use different properties, you need a paid GA account to roll them up. Needs more research, but it would definitely be neat.