Separating lithium ion cells for charging
No this won't work because the output from the chargers is not electrically isolated (transformer). The chargers will all share a common ground so the positive from charger 2 will short circuit into the negative of charger 1, and charger 3's positive will short circuit to charger 2's negative.

Your diagram isn't entirely accurate according to the datasheet for the TP4056. The sample wiring diagram on their datasheet clearly shows the battery negative tied to ground. Your diagram shows the negative isolated from the charger inputs which suggests some sort of isolation, but that's not the case.

If you want a quick and dirty way to charge your batteries in this configuration, then I suggest a linear charger monitored by an op-amp or comparator. It's by no means the best way to charge a battery, but it's safe and might be what you're looking for. Here's something to get you started. NOTE, the values and components here are arbitrary. This is just something I threw together.