Don't know about Netgear stuff, but, the D-Link non-wireless modem/router I have doesn't need anything conneted to it to maintain the ADSL connection. Once you set up all the ISP details in the modem/router (usually via 192.168.0.1 using a browser) you should be able to unplug or switch off all other peripherals - just leave the modem/router switched on and connected to the line.
ST