I am not familiar with this module so without the schematic it is difficult to assess whether there is anything extra around the GPIO16 (D0) and RST / EN circuitry that may cause wake up problems.
I would say, however, that if your goal is to use deep sleep to efficiently extend battery operation then this type of module with usb and probably an inefficient regulator is not the best idea. This is because even with the esp8266 in deep sleep there will be significant current drawn by the peripheral circuitry.
For optimum battery deep sleep you want to use a raw ESP-12E/F module combined with an efficient LDO or switching regulator.
Thanks from all the suggestions.
Regards,
Roberto