I have a system that runs on 3.3V and I want to run it off a single 3.7V Li-on cell. I am planning to use a 3.3V LDO such as the BU33SD5 to lower the battery voltage. However I also want to charge the battery in-circuit from USB. My current plan is to use a MCP73811 to charge the Li-po at 85mA. So I would connect the VDD (power in) pin to the VBUS pin on the USB port, and connect the battery AND system-load (ie the LDO) to the VBAT pin (const current/oltage out). The obvious downside of this is that when charging, if you use the system then you may be stealing some of the 85mA charging current.
USB -> MCP73811 -> battery in parallel with LDO -> system
As this is my first rechargeable battery project, I just want to be careful that I don't do anything stupid - so is this a reasonable solution?
Is there a more elegant way to do this? Perhaps some kind of integrated solution that separates the battery from the system load and generates the 3.3V either from the battery or the USB voltage (depending on the situation).