Hmm...it can still cause problems. Granted NAT would track Public traffic to private traffic, but your routing tables would over ride DNS and your DNS cache would cause issues. So say Milk.com was at 6.1.2.3, and a computer A on your network wanted to go to it, it would ask your router where Milk.com was and your router would to a DNS look up and answer 6.1.2.3 and you would get to Milk.com and computer A would store that IP in it's DNS cache. But say IP address of computer B was 6.1.2.3, when computer A would next try to go to Milk.com, it would say "oh I already know how to get there" and send traffic to 6.1.2.3, the router would take that request and send it to computer B. So that's one problem. Never-mind how it would effect the loop back in computer B's own routing tables. Overall it would just be messy.
More to the point, what is the benefit of using such a range?