Please don't.You can put 2 dns addresses in there. It says "DNS server addresses, in order of use". So in theory, if the first doesn't give a result it tries the second. You could just make sure you put your internal dns server first in the list, and as long as the internal dns server isn't able to resolve external addresses I think it should work. Give it a shot and let me know!
Set up your DNS server correctly. Either configure your ISP as a forwarder or use the root hints. Point the clients only to the internal DNS server.