You know everybody is different and their systems are going to react different. If lack of protein on the MC caused hair loss I'd be bald so would all the thousands that have done the MC and Sy Sperling the gradual hair replacement guy on TV would be out of business cause all folks would hafta do is start supplementing with protein so they won't loose their hair.
If you do the maximum number of drinks that would add up to 1200 calories which is hardly "starvation". Between the lemon and the syrup you are providing pretty much just about all the vitamins and minerals you need plus readily assimilable carbs that will give you energy to cope with everyday activities. Personally I would think the protein drink would keep the digestive system active. It has to how else would it process the protein.
Are you *absolutely* sure that the hair loss happened on the MC?. I've been on this forum on and off for 3+/- years and have never heard anyone claim to have lost hair on the MC.
The MC is not the only way to detox if you are absolutely sure that you are loosing hair on the MC I would consider trying a juice fast.