Can I use Realm.io to store things in the cloud that a tvOS app can use an API to GET to the info?
Yes you can use Realm.io with tvOS. You can use the Realm Database locally on your Apple TV and the Realm Mobile Platform on your server or cloud. Realm Mobile Platforms API Bridge gives you the opportunity to connect it "to existing systems and APIs."
See the docs:
https://realm.io/docs/swift/latest/#tvos
And mobile platform: