Have an Australian eVisa since they came into being. NEVER has anyone question the fact it is not in the passport. Not even ever been asked to show evidence of having an eVisa, booking, online check-in, counter check-in, bag drop or at the gate.
The very first time I used it I came armed with every bit of info possible from letters of grant, 24 hour phone numbers to call etc if questioned but never required. A seamless process.