That model you linked does not appear to be USB-C.
Saw this on Apple's site:
USB-C to USB Adapter
The USB-C to USB Adapter lets you use any standard USB (USB-A) device or hub with your MacBook. It provides data transfer and power to USB-A devices. For example, you can use this adapter to connect your MacBook to a:
Portable flash drive
Hard Drive
Digital Camera
Powered USB 3 hub
USB to Ethernet adapter
USB to Lightning Cable for charging and syncing your iPhone, iPad, or iPod
The USB-C to USB Adapter supports data transfer at up to 5 Gbps (USB 3.1 Gen 1).
So, on paper it is supported, though I suspect using Apple's adapter will be a must.
They also support USB target disk mode, too. You could just use a USB-C to USB-A cable.
You can also NetBoot over WiFi on most recent (2011+ maybe?) Macs. It takes longer, but it might satisfy an occasional need without needing to buy more adapters.
For the record, Belkin has announced a USB-C to Gigabit Ethernet adapter, but there's no shipping or price info just yet.
More info here.
typing usb-c gigabit ethernet into google produces many prices.