Android Wear on CopperheadOS?

I don't believe Android Wear works at all without Google Play Services, neither at the moment with MicroG (which is not recommended for CopperheadOS anyway as it introduces a security risk due to it requiring signature spoofing), though support is planned for sometime in the future.

Gadgetbridge, which works for Pebble, Mi Band and a couple other non Android Wear devices, doesn't support Android Wear yet either.

There is AsteroidOS, an open source alternative for Android Wear, which completely replaces the OS (unlike Gadgetbridge which just interfaces with the pre-existing one). However it's in very early alpha, and thus only supports a very limited amount of devices, the LG G Watch (W100) of which being the only one yet to support notifications.