If you don't manually specify DNS servers on the WAN connection then the DrayTek hands out itself as the DNS server to LAN clients, regardless of which DNS servers end up being allocated to the WAN.

However, when you attempt to resolve names where the DrayTek is set as your DNS server this results in a 2ms timeout error before the name is returned. I assume this means that the 2820 doesn't even cache resolved names but is just forwarding the requests.

In this case is there any reason to have clients look to it at all, better to have them go direct to the external DNS servers?

I suppose it would make sense of you were using the WAN failover feature.