Possible to connect WiFi router to a X1 TV box HDMI out port?

The purpose is to avoid having to buy another modem/router for my garage's Lorex camera security system, which would entail getting another bundled internet account from Xfinity, with unneeed voice and TV service and for another $120. Only one modem/router allowed for the whopping $254 plus a month I already pay. 

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@Monopolio wrote:

Could I use an HDMI to Ethernet converter cable to connect the X1 TV box's HDMI out port to a WiFi router instead of a TV? Would the WiFi router work as expected? Thank you.

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what is your need to connect. example: I want a longer run of HDMI to connect my set top box to a TV 25 feet away.

Only one modem/router per account, yes; and if you want another direct internet connection, you must get their bundled product with unneeded services like TV and voice. I'm using another WiFi network that is connected to their modem/router gateway. It works fairly good. I'll stick with that. 

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@Monopolio wrote:

The purpose is to avoid having to buy another modem/router for my garage's Lorex camera security system, which would entail getting another bundled internet account from Xfinity, with unneeed voice and TV service and for another $120. Only one modem/router allowed for the whopping $254 plus a month I already pay. 

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what do you have running between the garage and the home now? (coax only? outside rated ethernet buried/arial?) distance of the run? does your cell phone work in the same location as the camera connecting to the home wifi?  does camera need ethernet or wifi? bandwidth?