Is the kernel flashed automatically from CWM? By this, I mean, while flashing a firmware (update.zip) from ClockworkMod recovery, is boot.img also flashed or do I need to use fastboot separately?
What does the developer say?

Seriously every single rom that I've ever seen contained detailed instructions and more often than not a faq of some sorts for this reason exactly.

Anyway, if the zip file contains a boot.img file than it's safe to assume that it will be flashed. The updater-script that handles the copying of files is generated automatically when the rom is compiled so unless someone removes it, the kernel will be flashed.