[MrMars]

If my iMac is connected to the internet via both WiFi and Ethernet is that a problem? I feel if possible, being hardwired is always better than WiFi but it seems the ability to “unlock with Apple Watch” needs the WiFi connection.

[Tartarus]

There is no harm in doing this. There are no other benefits of having both than unlock with Watch, though.

[Trees]

Details in the Apple Community Support discussion below may help. There are other articles from other technical sites, but don't think we are allowed to list them.
https://discussions.apple.com/thread/7897850

[Just_Me_D]

If my iMac is connected to the internet via both WiFi and Ethernet is that a problem? I feel if possible, being hardwired is always better than WiFi but it seems the ability to “unlock with Apple Watch” needs the WiFi connection.

No sir, it is not. I’m connected in that manner every day while at work. One connection will override the other.

[Lee_Bo]

Doesn't hurt anything. I do the same thing with my MBP since I use my watch to unlock.

[Ipheuria]

Well it depends how you use it. If you’re using it at home then most likely not. If you’re at work it will depend how the network is set up. Where I work the Wifi is provides to clients and outside users so it is separate from our LAN. When our users are connected through both it sometimes will cause havoc with their network mappings. If you’re at home ofcourse none of that matters. You could always test it if you’re worried. Just go to speedtest.net and test the speed connected to both then only on ethernet. See if there is any difference and there’s your answer.

[Quis89]

No harm. As mentioned above, one connection will trump the other. You can set your service order and determine which connection you'd rather have as your primary. By default, I believe the ethernet connection will over-ride.

[dcoke22]

Pretty much all the Continuity features require WiFi to be enabled.

https://support.apple.com/en-us/HT204681

That's somewhat more than just unlocking with Apple Watch.