Short answer is "yes". When you are avoiding carbs temporarily to lose weight (an effective means of doing so) you are also avoiding certain foods that have the vitamins/minerals your body needs. For example:
- Many fruits are high in vitamins and minerals not found in protein sources or vegetables, or at least have them in higher concentrations. Unfortunately, most fruits are also very high in carbs. Such as Vitamin A.
- Some low carb diets also restrict dairy, which contains fat-born vitamins that our bodies need such as Vitamin D, as well as it being a good source of calcium.
- Some high carb vegetables also are a great source of potassium, but they will be off limits for a time.
The risks of not taking a multi-vitamin supplement are the same as if you are deficient in those vitamins. The most common problems that both my wife and I experienced in our low carb weight loss journey when we were not faithful with the supplements were:
- Decreased energy. Do note you will have decreased energy and "extreme hunger" for the first few days after switching to low carb. After that your energy levels return. Your body tends to hold your metabolism until it gets all the vitamins/minerals it needs to complete it. That means a reduction in energy until you get caught back up.
- Cramping/muscle pain. This is particularly bad if you don't have enough potassium and calcium.
- Headaches and general icky feeling. This is a little different than just being sick (which is always a possibility no matter what your diet). I can't tell you which deficiency causes this, but when you get back on the stick with the multi-vitamin it goes away.
Also note that when you exercise, your body will use those vitamins and minerals in greater quantities--no matter what the diet is. You very well may have to supplement even when you are maintaining.