First off, the Fat Fast sucks. It's effective, but not stupid.
"The measure of a diet should not be how miserable you feel while on it." - Chris Shugart
The fat Fast, as originally laid out by Brock, is more of a test of will power than it is an effective fat loss regmine. There are many, MANY better ways which are much easier.
For example, if you're into extreme dieting, check out Joel Marion's "Cheater's Diet" article.
If you want a moderate approach (which will NOT leave you feeling like shit and lifting half your previous poundages), try the T-Dawg diet.
Either of these options have been highly effective for many people, and they are a lot healthier.
However, to answer your question:
If anything, consuming whole foods in addtion to the whey/flax mix would make the diet MORE effective, and I would recommend it. The thermic effect (TEF) of whole food is much more substantial when consuming whole food as opposed to liquid meals. The increase--albeit slight--in your metabolic rate should facilitate in getting lean.
Hope this helps.