Can fake AirPods Gen 3 have AppleCare and a real serial number?

Re: “… but the price look too good to be true …”

Then it almost always IS !!!

Valid serial numbers can be easily counterfeited.

See related user tip here:

The All Too Common SAD Reality of Buying … - Apple Community

Hello ~ Do you have the serial number? If so click on link provided above and here and see what it tells you.

Check Your Service and Support Coverage - Apple Support

~Katana-San~

There is no such thing as AirPods Pro 3

Look here…

Check Your Service and Support Coverage - Apple Support