Short answer: no.
Long answer: no. Even if you wait until the new phone comes out, they'll have plenty of current ones to replace yours with. The fact that stores are out of iPhones for sale right now doesn't mean that Apple has zero iPhones on their hands; they have a good supply of existing models for this very purpose - replacing your "old" iPhone.
At some point in the future, they'll run out of them, but that won't be for quite a while. At that time, they'll try to fix your iPhone first before handing you a newer model.
With enough whining, they *might* give you a new one as a replacement a few months after it comes out, but that's unlikely.