whether it works or not....
or if it works, will it charge and play at the same time (or not)....
why would you consider something else....
especially when there are other PSU that have been tried and tested (and work fairly flawlessly) in 100s of builds
my advice, if you lack the knowledge in certain departments go with whats tried and test....
its a waste of time and effort looking at things you dont have good knowledge off (theirs a reason the other two are the most used)
put your effort in to making your builds functional and as clean as possible....
That doesn't look like a power supply to me, just a battery charger. Meaning you'll need a separate boost converter. Stick with the adafruit powerboost or the banggood model, as they are both 'tried and tested' by many here and will be able to help you with the wiring.