Powering a circuit from either USB or LIPO
Your thinking goes in right direction but the choice of components could be better. The task of charging single lithium battery from USB and powering system load at the same time is so common nowadays that there are literally dozens of chips designed exactly for this purpose.

What you are looking for is called "Power Path", and it is a technology that allows input power distribution between charging and system load, powering system from the battery when external adapter disconnected and even boosting external power with battery when system draws more current than available from adapter/USB.

Note, however, that while they all have either LDO or switching buck to get input voltage down to battery charging voltage, they do not have another one for 3.3 V. So, they usually output either regulated 4.2 V or direct cell voltage. Considering your 800 mA maximum system load I'd recommend using buck converter rather than LDO.