Yes, the 'high-end' counterfeit AirPods are so good, they show up in iOS with identical set up flows; battery indicators; feature support (at least claimed to iOS), etc. I'm not sure about AppleCare though.

The packaging is basically identical, unless you carefully scrutinize font DPI or alignment.

Have a look at YouTube videos; for a good AirPods counterfeit it's genuinely hard to tell things apart.

1. You’d be surprised at how good counterfeits can look nowadays, including packaging

2. If you’ve never seen/held the genuine item or don’t have them side to side, it can be very difficult to tell which is the genuine one