Does Adafruit PowerBoost 1000 Charger support data transfer? As the title says - Does Adafruit PowerBoost 1000 Charger support data transfer?
I mean that if I connect USB on one side to PC and Arduino on other side - can I still program it and get serial monitor communication?
Are the data lines connected??
No it doesn't.

As you can see from the schematic the incoming data lines aren't connected, and the outgoing are wired through appropriate resistors to set the current availability.