Does MCP73832 disconnect the input from the battery?

Folks,

Do battery charge controllers usually disconnect the input from the battery, when the external supply voltage is not present? In particular, I'm looking at MCP73832.

The datasheet says:

5.1.1 BATTERY MANAGEMENT INPUT SUPPLY (VDD)
The VDD pin is the input supply pin for the MCP73831/2 devices. The MCP73831/2 automatically enter a Power-Down mode if the voltage on the VDD input falls below the UVLO voltage (VSTOP). This feature prevents draining the battery pack when the VDD supply is not present.

Click to expand...

I wonder if power Power-Down mode includes disconnecting the battery from the input. The block diagram (p.2 in the datasheet) shows a MOSFET that could do the disconnecting.

I'd like to connect a voltage divider to the external supply voltage (upstream of the charger) in order to be able to detect the presence of external power. My concern is that the voltage divider could drain the battery, if the charger doesn't disconnect input from the battery.

The STAT pin on MCP73832 is asserted only when the battery is actually charging.

Any suggestion, insight or reference is really appreciated!

Best,
- Nick