Curious about something similar myself, though I'm pretty sure the answer (to my question at least) is that I can't do what I want to do with caching enabled.
I have two subsections of responsive code in header.php -- one that loads for mobile browsers and the other for desktops/tablets. I assume the reason those aren't working as intended for logged-out users is that it caches and reuses whatever version the very first visitor loads...if the first visitor is on a mobile device, the mobile version of the code is cached and then presented to everyone thereafter, no matter what device.
So would I be right in saying there's no way (as bcwint00 and I hope to) to disable caching of a section or the loaded contents of a template file?