Nope. And the transformers are never synchronized, even if they were certified as matching. They are separated when properly connected to an isolator, hence the name.Just another question here.. If both chargers share the same power cord (AC), would that synchronize the transformers?
Keep studying. There is a lot of theory to learn, but keep at it.
Maybe you can find some good circuits-book or websites that are made for teaching circuits.
Regardless, a commercially-produced solution sounds best for your situation--either an isolator, or a single-charger.