NO! Anyone on this forum will tell you that. The whole point of the cleanse is to give your digestive system a rest. By eating foods, whatever the amount, you'll be bypassing any good effects.
If you're having trouble with not eating anything, maybe you want to do a raw food diet or something of the sort and gradually ease into the Master-Cleanse by decreasing the food quantity till you're not eating solid foods? Once you're not eating solids, you can switch to the MC.