Firmware update and data exchange using ethernet
I guess you have never written bootloader until now, so I try to highlight how it works. 

Bootloader is a regular program that run as a first program - that means then after processor reset, the processor jumps to an address denoted by the reset vector, which is typically address 0x00. That is where you place your bootloader.

Then bootloader does all the configuration it needs to perform its tasks. In your case it will be configuration of the Ethernet port. 

After the configuration the bootloder checks if there is any new firmware to update. If so, then it downloaded it from Ethernet and programs the MCU's flash, from the point in memory where bootloader ends (so it doesn't overwrite itself).
And then the bootloader does the jump to where the actual program starts.

If there is no need to update the firmware then the bootloader just does the jump to actual program.

So, whether Ethernet controller is used only for bootloder or not doesn't matter. Bootloader and the actual program are a bit like separated programs.