Since which Android version can you use Ethernet through the USB port? Which makes are repotedly work with CyanogenMod?
That is dependent:


The kernel, along with the appropriate driver
Chipset support for USB OTG


The general consensus, if the kernel is modded and has support for OTG provided the handset supports it, then it will work alongside with the appropriate OTG cable with power support.

It might need custom modifications to Android to make it aware of OTG facilities if running on pre-Honeycomb Android versions.

However, since Honeycomb (Android 3.0) and upwards, there is USB facilities integrated into the framework which makes OTG mechanism even easier.