Although I'm assuming this particular combination doesn't provide favourable enough economics (or it would probably be a household name already), I can definitely see how this approach in general could. You could have the best of both worlds: cheap, but slow charge/discharge storage combined with the ability to very quickly scale up to meet peak daily demand for a limited (but sufficient) period of time.
EDIT: here we go - http://www.nature.com/articles/srep04315 . Lithium iron phosphate batteries (LiFePO).
Although I'm assuming this particular combination doesn't provide favourable enough economics (or it would probably be a household name already), I can definitely see how this approach in general could. You could have the best of both worlds: cheap, but slow charge/discharge storage combined with the ability to very quickly scale up to meet peak daily demand for a limited (but sufficient) period of time.