well yes that's exactly it. what you're much more likely to do is say that your firewall is facing the internet. any hits on the firewalls ip address for port 80 will be forwarded to the squid server. that then just uses it's own largely default caching logic to know whether to send the request on to the destination or not, just like any other caching operation. well, nearly just the same, only difference is that the squid box will recieve standard http requests not http-proxy requests, but other than that exactly the same rules apply. also you can look at using squid as a fornt end to a number of seperate boxes, either identical clones or not, to allow a more resilient architecture.
you're wrong to really be asking about a DNS entry or anything, not really relevant. if www.domain.com
resolves to a box that runs squid on port 80, what else do you think is going to happen? but as above you would have these boxes on a private LAN with a decent firewall having the actual internet ip addresses.