The best proof would be to just try it yourself and see what happens. Load up Wireshark, make a query, and look at your traffic. Because the problem is there isn’t a single technical article I can point you to that details exactly how DNS resolution works on every device running any given operating system. “Network attached devices” could be anything and so you can’t be certain exactly how each device will operate.
I’ll give you that in the case of Windows devices specifically, Microsoft isn’t good at keeping documentation up to date, and on older version of windows it used to work the way you describe. It would send the request to your first DNS server, wait one second for a response, and only if it didn’t get one would it move on to your next one. However in Windows 10 today if I edit my configuration so that I use a local DNS server located at 192.168.69.210 as my “Preferred” DNS server and 1.1.1.1 as my “Alternate” DNS server look what happens:
It sends the same request out to both without waiting and the response from Cloudflare actually comes in before the one from my local DNS server. So if this were a request for a blocked domain, the client would accept the response from Cloudflare because it was received first and so the request wouldn’t be blocked.