No, I do not think that Amazon use a FIFO approach. Firstly, they will assume that all units for an ASIN are the same (technically according to the rules, new versions of products should have a new ASIN). Therefore to Amazon it won’t matter which one they pick and send because they are all the same.
More importantly, they will pick the unit that they can send for the cheapest fulfilment cost and the fastest fulfilment for the customer. So, most of your inventory will be distributed in various warehouses across the country so that they can pick one from the warehouse that is closest to the customer. Maybe that specific closest warehouse has old versions while the other warehouses may just hold the new version.
So, you have to assume that new and old versions are mixed in together which means that you really have no way of knowing when you have sold out of all the old version.
Can I ask what the status of the new version is? Is it already at Amazon? Or is it still being produced in China?