One of the things I found out was that several of my supplements had hidden carbs in them either by way of rice flour as a filler or vegetable matter as part of the capsule. Make sure you check the ingredients on the bottle.
I have to take iron as I'm anemic and not taking it is not an option. I do my program through a doc and he told me to be sure and continue my iron supplements. So, for that one, if you need it, I'd say take it.
I take other supplements including Vitamin D and I think I have had better results than if I didn't take them because I feel better. In the carb sensitivity book I'm reading, vit D was also linked to being able to burn fat.
If in doubt about what you are taking, give a list of all supplements and prescriptions to a pharmacist and they can pin point any possible conflicts.