There isn't any indication in the CoolpadIndia website that Coolpad Note 3 is tested with its compatibility for Ethernet Adpater. But the way these Adapters work, it implies that they should work generally with any Android Smartphones, though the Androids do not have any external indication of connection through Ethernet.
But here is a way though to test it yourself, if you have an Ethernet Adapter with you. Go for the Airplane mode, and now try to connect to the Internet through the Ethernet Adapter . If it gets connected, then it is proved that it is compatible with an Ethernet Adapter.