As long as your existing Reservation falls in the same category and size, ie D2S or the specific number of cores, and the Reservation scope (ie Subscription, Resource Group) it should flick over once the old one is turned off. You may find yourself running a mix of reserved instances and Pay As you Go while both VMs are up and running.
Azure Reservations are based on Compute (ie 2 vCPU, and Family - ie D2) and not by OS.