We have a customer that is looking to use a BizSpark license in our cloud. As this is MSDN, I don't believe this is valid unless it is hosted in Azure. if we dedicate hosts to our customer and their workloads, would this be valid?

Correct - BizSpark don’t have “license mobility with SA” rights to run on a shared hardware environment except on Azure.

However, you may run them on a physically dedicated hardware for the end-customer.