MCP73871 Battery Under Voltage Protection
On page one of the datasheet it says:


  The MCP73871 device includes a low battery indicator


There is no mention of battery protection anywhere.

If your design uses the Low Battery Status Indicator (LBO) signal to shut down the circuits which drain the battery then I do not think you need extra battery protection.

However, it might be complex to guarantee that this will work properly under all conditions so it might be a good idea to simply add a battery protection circuit. A circuit based on the ubiquitous DW01 comes to mind. If it was my design, I would simply add that battery protection to cover my behind ;-)