I just flew PHX to LAX to SYD (in SYD airport now awaiting my next flight). I had no problem checking in on the app and getting a mobile boarding pass. I was also able to print at home. Passport was checked at the gate which is normal. Not one time did I have any problem. You have to do the ETA for Australia so not as difficult as other countries (from what I hear). So it is possible to travel internationally and check in at home but as others have stated it depends on your destination.