As long as you're presenting GC and extension letter to airline and CBP, you're good.
I just don't think online check in for international flight is the same as online check in for domestic flight. The whole point for me of checking in online when travelling domestically is to never see an agent. For international flight you gotta see an agent regardless. In addition, you're never fully checked in, as it asks to "complete check in" at the airport. Hense I was curious about your experience.