Unfortunately, the latest versions of Squid are not SMP-aware (as referenced by their core developers), and running it in front of Apache2 yields a significant performance decrease.
I did a lot of thorough tests on this exact point. I've run Squid in front of Apache 1.3.x for years, and found roughly a 400% increase in request response time on a uniprocessor machine.
When I moved to Apache 2 on a dual-core SMP machine, I tested Squid in front of Apache 2.x, and found that my request responses dropped 75% as compared to Apache 2.x running natively on port 80. Apache is able to thread processes across multiple cores, but Squid is not.
I do, however.. have an internal Squid server running on my BSD machine, which ALL outbound traffic going across port 80 is transparently redirected through (redirected at the router by some iptables rules), so my HEAD requests are already going there. I don't see any significant increase or decrease in performance when enabling or disabling that capability.
It is an interesting idea, but I don't think it applies to this specific problem.