Ethernet Z-wave controler

Yes, you can. But after that you may have to restart the Z-Wave binding manually to get the temporary disconnected controllers back to life depending on how your controllers are connected to OH.
If you use my actual combination with hub4com as Windows serial client on OH server and ser2net on Raspi as serial server then this is no problem. The network will immediately recover as soon as the connection is reestablished.
If you use however different Serial-to-IP solutions (e.g. Silex USB-IP server which I used before), then a short interruption will kill the connectivity of the controller to OH and it will only come back if you restart the Z-Wave binding or OH. The same is also true if you have your stick directly physically connected to a COM Port on the OH server.

I want to bring up the original question of OP: is there a off-the-shelf z-wave controller with ethernet (or maybe wlan) connect that is supported by OH3?

I know there are solutions with usb2eth or sharing the usb of pi, but i want a stable, ready-made solution. Similar to the hue-bridge, i just want to plug it in and be happy.
Reasons for me are that the diy-solutions fail from time to time (tried sharing usb over eth) and the host “looses” the usb port, resulting in needing reboots. Also i want to place the controller in the middle of the building, not in the rack in the cellar where it needs two extenders to even reach the devices.

edit: e.g. do the fg322 gateway, the devolo or the delock work well?