How can I tell if my Samsung S7 supports connecting to a wired ethernet via a usb OTG cable?
Like any other computer system Android also requires a driver for talking to a device. 

However unlike regular PCs you can't just install a driver, instead you only have the drivers the manufacturer included when building the Android system.

In a terminal or on an adb shell you can list all the drivers that were included in your kernel:

ls /system/lib/modules


If the list contains for example the driver usbnet there is a chance that an USB Ethernet adapter may work.