Using Google DNS doesn't make privacy protection tools useless.
To begin with, Google is far from the only advertising network around (although it is by far the biggest). Google DNS won't help other companies than Google track you at all.
Secondly, there is only a limited amount of data that gets sent to the DNS server every time.
Once a DNS request gets sent to the DNS server, the DNS server has the following information:
Your IP address requested the IP address associated with the domain name at time on date.
203.0.113.77 requested the IP address associated with www.example.com at 00:00:00 UTC on 1 January 1970.
If you are behind NAT, the DNS server will not be able to distinguish you from other users on your network.
So how can Google use this information? Of course, they could use it in ways that do not affect your privacy, such as getting an impression which web sites are popular globally.
However, Google does keep a record of your visits of every web site that displays their advertisements / trackers / widgets and how you interact with these.
If you repeatedly visit a web site with their advertisements on it shortly after a DNS request for that domain is sent, they can then associate your visits to those domain names with that record. They may then be able to associate other DNS requests from your IP address with that record.
Furthermore, although to my knowledge Google doesn't do this at the moment, they can associate the record of your actions on web sites with their ads and trackers with any Google profile you may be logged in to at the moment, so they are able to associate those visits to your name (and maybe the home address you have set in Google Maps).
If they know you visit certain web sites, they may be able to refine the selection of the ads served to you based on the content of certain sites. But domain names are not complete URLs. They only know you visited travel.example.com, not that you visited http://travel.example.com/holidays/Somewhere. Therefore, the data they get from your DNS are much less precise than what they could have gotten from tracking code on the page itself.