Does a phone's battery charge when in download mode?
It will charge, but you may not have "charge full" indication , so monitor charging so that you don't end up charging once it is full ( batteries do not charge once full but internal temperature goes up, which is  not good for battery life). Charging for 90 minutes should comfortably see you through flashing activities

To understand more about about charging,see BU 409-Charging Li Ion and other linked sources referred