I think most routers set themselves as the DNS server, so NAT is not in effect (the computer only sends the request to a local address) unless you define a custom DNS server, which isn't common for home users.
That said, I've never seen a router that didn't allow UDP packets to flow back to the origin client.
> I think most routers set themselves as the DNS server
DNS forwarders like dnsmasq are a relatively recent inclusion in home routers. Sure, they've been there for 10 years or so, but they weren't there for the 5+ years before that. Before Linux took over the embedded OS on home routers, the DHCP servers just passed the DNS configuration that the WAN port got from the ISP, and you can still do that now if you want. That's why nslookup.exe and dig still work on your workstation when you specify an external DNS server instead of the one your DHCP server on your home router gives you.
> That said, I've never seen a router that didn't allow UDP packets to flow back to the origin client.
That said, I've never seen a router that didn't allow UDP packets to flow back to the origin client.