The answer is, yes you can, as long as there is an Ethernet IN port which it SHOULD definitely have, you most certainly can. I know this because I DO THIS with my modem/router combo, there is no COAX hooked up to it. I have a modem already AND a wireless router, I just needed one to extend my range so what I did was grabbed my old modem/router combo with the same question in mind, ran an Ethernet from my current wireless routers OUT to my modem/router combos IN (it has four ports all act as an IN AND an OUT) and to my surprise I had a signal. Then I proceeded to enter the password and logged in. After that just to confirm I browsed the web and even downloaded an app on my phone, and it worked perfectly fine. Although these routers tend to be on the low end side it got the job done, and now I have two access points in my house. You don't like to use range extenders or repeaters because it takes away from your current bandwidth/strength.
To answer your question if it has an IN or not, you can tell simply by looking to see if it has a yellow ring or LED light, if so, that it is an IN and if green or blank it's an OUT. Mine has both a yellow and a green LED on each one and the light will blink according to which way it's hooked up, in this case "in", so it flashes yellow.