Loss of WAN connection with Genies

I have an HR 44 receiver with several Genie G41-500s throughout the house. Each of the sets using a genie is also connected into the wall through coax.  I also have Verizon FIos for intenet.

Currently, at my Verizon router, there is a coax cable coming out of the wall that goes into a DirecTV Connected Network Adapter (see image). An ethernet cord comes out of the CNA and into the WAN port on the current router.

I am changing routers, and will need to change the location of the router to a spot where there is no DirectV coax feed. Can anyone tell me what will happen if the coax feed is no longer connected to the router through the CNA? Will the Genies be ok, as they are also connected through coax? They are currently working with this set up. Thank you.