What kind of power management circuit do I need to embedded a rechargeable battery in my electronics project?
Yes, but adding the device load directly to the charger load could confuse the charger IC. A better idea is to implement the load sharing system described in Microchip's AN1149: "Design A Load Sharing System Power Path Management with Microchip's Stand-Alone Li-Ion Battery Charger". This will run the device off battery power when it is standalone, and switch transparently to wall power when external power is available.