Unless you know what the DNS request is "supposed to return", you can't know that just getting any DNS response indicates that you have full Internet connectivity.
Sorry, you were imagining the use of a TXT record (I assume) and that would work better than an A record inquiry that I was considering.
It still wouldn’t find http filtering, but it would work better than I initially gave it credit. (I still doubt it would give a contextually correct answer for an airplane wifi connection [where DNS May very well work but few other services do if not paid].)