What you didn’t mention was how these are connected. Is the wired router connected to the wireless router using its WAN or LAN port (there’s a difference)?
[wireless router](lan)<-- wire -->(wan)[wired router]
The above creates a firewall between the two subnets represented by each router.
[wireless router](lan)<-- wire -->(lan)[wired router]
The above does NOT create a firewall. All devices share the same network. And now it gets complicated because you have two DHCP servers on the same network, so one of them should be disabled. If you don’t, then it’s pure luck which DHCP server responds to client requests across both routers, and clients will be arbitrarily configured for one of two subnets, one of which is probably not connected to the ISP (not good).
So there definitely are implications to connecting devices, and how you connect them, both in terms of functionality and security.