No. The ReeCharge case has a separate input and output charge button that only allows charging from the Dynamo Hub to the ReeCharge Case OR from the ReeCharge Case to your iPhone.
Please note that the ReeCharge input charge will override the output charge to the iPhone. If the dynamo hub is sending power to the ReeCharge Case (even if the input charge button is turned off) while it is charging your iPhone, the system will stop charging your phone and charge the ReeCharge Case. To prevent this, please plug off the cable from the ReeCharge Case while cycling.
Consumer Advice: Do not start cycling with an empty iPhone AND empty ReeCharge Case.