So, are you saying the Synchronizer itself doesn't necessarily need the desired nature, just the (knocked out) Pokemon in your first/lead party slot?Yup, the bug SOS Call chains and Synchronized is now confirmed.
When you send a Pokémon with Synchronize on the field and chain for allies, the allies will be affected by Synchronize.
However, the nature that they will have 50% of the time is the nature of the first party Pokémon.
The first party Pokémon can be ko, it still works. (I have a Naughty KO Munchlax and the 4 Pokémon I caught were all Naughty).
The Synchronizer can lose its ability with Roleplay/Skill Swap, it still works.