Yes, it should be fine. I have seen several power banks that do the same. Since the TP chips do CC output, they share current well but the end termination stays at 0.1A (defualt of the boards) as the last TP chip with the highest output voltage tolerance will stay on last.
The diode is fine as long as you use a decent rated schottky. The TP chip is a low dropout regulator so I think if the input to the chip is 4.5V or more then it should be fine. Diodes are required if you plan to do what I do using only one if a slow charge via usb port is an option, if not then simply paralleling all would still work.
Do keep in mind these things need heatsinking to work best.