1.) if Alert pin is triggered (low), battery will be disconnected.
2.) if VBUS is HIGH, battery will be reconnected.
3.) From Point 2 on, the MCU will reset ALERT and battery stays connected even if VBUS Signal is low again.
I am not sure how this applies to an Arduino. Your transistors are in a 'or' configuration and the battery will be enabled as long as either the Alert\ or VBUS_3V3 is high. You have to take them both low to turn it off.