Not necessarily, this depends entirely on the router. Not all routers accept DNS traffic on port 53.

If you have DHCP enabled on your clients, the router will assign its clients the DNS servers that *it's* receiving via DHCP from your ISP. Do an ipconfig on your clients on you'll likely see that their DNS settings are pointing at your ISP's DNS servers, not the router itself.

There is a difference between a routers ability to accept nameserver traffic on port 53 and forward it to an upstream DNS or root hints server vs. it's ability to hand out DNS settings via DHCP. This is why I recommended to the OP that leaving his clients DHCP enabled is the safer solution unless he has knowledge of TCP/IP. If the OP follows your advice than he would have to manually change his IP config anytime he wants to get online anywhere else.