No, the color developer is totally different. Color developing agent is different (CD-3 versus CD-4 in C-41), pH is different, it is very fogging and there are chemistry that fine-tune color balance and Dmax.
You WILL get positive images with any BW developer as a first developer, then light or chemical fogging, and then any color negative process (such as C-41) (dev, bleach, fix), so what you ask is possible, but the resulting image quality is far from E6. It is interesting experimentation though!
But, if you want "normal", high-quality slides with neutral color, deep blacks and bright whites and long-term dye stability, you need E6 first developer AND E6 color developer (and formalin somewhere in process). Bleaches and fixes can be changed as long as they are potent enough to remove all silver and silver halides.