Yeap, fine to use these external services as fowrders but make sure that the clients themselves still point directly at the DC as this handles all your internal DNS as well.
There are considerations around the uptream services messing with results or speeds as hinted to by enjay as each service will have its own priorities, we use 184.108.40.206 as a fallback for our servers with local ISP DNS servers which thankfully stay put but can have their issues too.
Think I'm being a bit dim.
Read through this thread and saw the recommendations not to have the DNS set in the NIC properties. So I decided to set our new network servers like that. I put the Google DNS in to the Forwarders section of DNS above the County ones, removed all DNS addresses from the servers and watched as the internet disappeared from them. If I push the County DNS back up to the top all works fine.
Am I doing something wrong or have county blocked other DNS providers?
If your port 53 isn't open then the latter.