Sure DHCP can serve many DNS addresses, but the question is: how many will your clients pick up from that.
Try connecting a computer like your typical client uses, and look in the network information to see what it has done.
Sure it would be an idea to try to reduce the list in DHCP to 2 servers, or to order them differently.
(your dns 1, google dns 1, your dns 2, google dns 2)
Depending on your config it may be possible to send some part of the clients a different order:
(your dns 2, google dns 2, your dns 1, google dns1)
The only way to know is to test it. There is no reason to test on your live system either, as there are plenty of ways you can mock up a config in a virtual lab.
Assign a test client with a selection of DNS servers, then create ACLs to block access to each DNS server in turn, and see how the client behaves.