Good news, yes, this can be done!
I've done a fair bit of this, both including Google Analytics (GA) and Google Tag Manager (GTM) in add-ons and HTML tiles.
Essentially you'll need to include the GA code snippet in the pages rendered by your app. I'd recommend taking into account somehow in your add-on config setting up the correct tracking ID for GA. You'll want different GA properties for dev/test and prod.
This will give you pageviews (hits) in GA for the pages rendered by your app. You may need to consider cross-domain tracking depending on what you're looking to capture around the context of your app iframes within your Jive instance.
You mention you have "tabs" and single page apps, in which case here you'd be looking to trigger additional "virtual pageviews" and events into GA to capture. You may want to consider sending additional hits or events to GA using the documented JS provided by Google.
I mentioned GTM early on, this is a great way of taking out the pageview and event tracking logic and code from you app. You'd add the GTM JS snippet instead of the GA snippet, and from there it's working in GTM to add GA and set up the pageview and event tracking you're looking for.
I hope that helps, keep me posted on how you get on!