I've gone through the steps to setup App Invites as described here.
Out of curiosity, I tried without including the google-services.json and it still works depending upon the configuration in Google Developer Console.
If there is no Android API key (or there is an Android API key but no package restrictions) then App Invites works (by "works" I mean is able to send the invite message - I haven't tested the other features such as referrals). If API key package restrictions are defined then those rules are obeyed.
UPDATE: Try this scenario - No Api Keys defined, Two OAuth 2.0 client IDs - one for release, one for debug. Then App Invites can send messages in both release and debug builds without any need for the json file.
Is this all expected behaviour? What benefits does including the json file bring?