I am going to a personal trainer 2 times a week to prepare for my wedding in April and I have stayed on the MC. I have noticed I am slightly weaker, but still able to handle the weight training. I didn't tell my trainer that I am on the MC, because she would freak out and talk about protein. So I am just "hanging in there" without too much trouble. After Easter I will be eating again and I will know if I was really weak or not while I keep training.
I think you can do it...just know your limits.