The NAT might cause problems, yes. It's assumed that all APs with the same ESSID (network name) are access points to the exact same network – when they're close enough to roam between, it's done transparently to the IP layer.
So what you should do is configure the C7 in "bridge" mode. Some firmwares have an actual setting to disable routing and bridge the "WAN" port along with everything else.
It seems that C7 doesn't, however, you can still disable DHCP and use the existing bridge between its Wi-Fi AP and the "LAN" ports. That is, you should connect both devices through their "LAN" ports and leave C7's WAN disconnected.