I wrote a lot of CMS type apps with Cake and was thinking along the same lines. I've tried Joomla, Drupal and Wordpress but still had a dirty feeling in my mouth that I was failing by using Cake just for the sake of it or vice versa.
The most important common denominator, in my experience, is the back-end. It is re-used most often, but gets the least input.
Now I have built my own CMS with CakePHP. The intention is to 'opensource' it, but it's not quite ready yet.
I don't think it is worth the headache trying to combine, then maintain Cake and a 3rd party CMS. Save your best modules and components and build your own. The blog tutorial will give you a good head start and you can cherrypick what you like from other sources, rewriting it to suit your ideals. The benefit is you will then know the CMS inside out and have it working just the way you want. You'll learn a lot along the way as well.