Have you? So what does it send back?
(You can easily check this with an app like Little Snitch, look for the browser connecting to IPs 8.8.8.8 and 8.8.4.4)
I also just noticed that Little Snitch actually does NOT log the dns requests. Maybe this is caused by Chromium using ipv6 to access google-public-dns-a.google.com ?
Anyway, I then installed Vallum (1) and with this app, in the log i see many of these requests: https://i.imgur.com/lUR3Fd7.png