The problem wasn't that I need to make HTTP requests when there is no DNS, its about behavior of my Perl programs when networks are disconnected.
For instance: If the PC disconnects from all networks, then any time the code attempts to do a AnyEvent HTTP request - it would block for 150 seconds - a complete block with the event loop no longer running. In that event loop I could be running things like AnyEvent:HTTPD to handle requests from a localhost user GUI, or I could have scheduled timers that I expect to occur within that 150 seconds, also AnyEvent Signal handlers can't run. So essentially the entire program 'freezes' for 150s trying to do the syncronous call to a non existent DNS server on localhost.
The correct 'fix' here is probably for AnyEvent::DNS to use AnyEvent::DNS::Resolver as per my solution - with the DNS default nameservers removed - to ensure the constructor can never go down a code path of making a DNS call via AnyEvent::DNS::Resolver.