There seem to be several potential technical spoilers to this theory.
1) Going to the DNS for every request is inefficient. Caching for some period would be assumed to be standard. That period could be assumed to be more than a few minutes.
2) ISPs with IPv4 using NAT may have several external IP addresses on multiple load sharing boxes. The ISP users' browser connections can be multiplexed on any of those IP addresses by dynamic source port assignments. A different destination IP address will have to open a new connection. There is no guarantee it will be multiplexed onto the same external IP address as previous ones from that user - even in the same session.