Yes, it will work. It's the lactose that gives the cheese/yogurt type bacteria the head-start needed to prevent the milk from spoiling. Those types of bacteria are everywhere (including your culture), so even sterilized milk can be made into yogurt or cheese.
I mix powdered milk in with my reg milk to make yogurt all the time... this added milk thickens the yogurt... just make it like you always would...
as for cheese I've never tried to make it with powdered but all I could find said you can use the powdered milk but it won't melt like normal cheese... I did find a video on youtube that shows how it's done....