It may work fine for a while, but you are likely to run into issues unless you follow Pooper's advice in the post below. Issues would arise from the Arris router and your personal router BOTH trying to assign IPs, and do NAT, and apply UPNP to the same computers.
BTW, if you have an Asus RT-N66U personal router, then you can put it into "Access Point Mode" in the settings which disables DHCP/NAT/UPNP automatically and as a bonus it lets you plug the input ethernet into the WAN port giving you 4 free LAN ports for your other ethernet devices (most routers require you use one of the LAN ports as input).
You don't need to use bridge mode at all. You just need to turn off DHCP, and UPNP in your router, give it a static ip address (outside the range that Cogeco's router uses to supply addresses to connected devices), and connect it to Cogeco's modem/router through its LAN port (not WAN). You can then turn off wireless completely in Cogeco's modem, and have it just do the routing while using the wireless radios from your router.
CogecoTivo+2 Minis, Samsung PN58C6500, LG BD590 BluRay, PioneerElite SC-05 Rcvr, Xbox One&360, Ouya, ATV1, WDTVLive+, PC