I would NEVER, EVER take a metabolism booster while fasting. That is just asking for a Schiavo-esque inbalance (IMO) since they deplete your electrolytes and can cause mineral deficiencies even when you've got food in your system. You really have to be careful not to do anything that's going to delete electrolytes and trace minerals too rapidly especially during a water only fast. That's why it's not reccommended to do anything that taxes your heart too much or causes you to lose a lot of water as sweat.
I have read a few people's posts who eat a little bit (usually lettuce) and then fast the rest of the day. I think the only problem is that you might get hungry since you'd still be digesting food. And part of the beauty of fasting is that you lose the physical desire for food after the first couple of days. Psychological? Now that's a different story.
Best of luck to you and let us know how it works if you try the eating/fasting combo.