I deep condition first sometimes and then I either co-wash or use shampoo after and it doesnt cause moisture overload on my hair. I believe that you should be fine.
I don't think it will cause moisture overload, but you could have some seriously gunky build-up...depending on how thick your conditioners are and how long you leave them on.
As long as you don't have any gels or loads of products on your hair. It is one of the best ways to get in that moisture. I usually wash and let my hair air dry and then apply condish.