To the OP, I may be missing something here but aren't you just talking about load sharing?
https://ww1.microchip.com/downloads/en/appnotes/01149c.pdfMost, if not all lithium chemistry chargers use current draw at constant voltage for charge termination. SO it charges at constant current, then when maximum cell voltage is reached, it holds that voltage, allowing the cell(s) to determine the current. As the cell charges, this current decreases, and "end of charge" is usually when this current is C/10 or C/20 where C is the charging current.
The upshot of that is, any load on the system also draws current, and if this is larger than C/10 - say you charge at 500mA. C/10 = 50mA, so any load greater than 50mA will mean the charger never stops, and could mean, that you're constantly putting energy into the battery even when it is at max capacity. Whilst this current may be small, and would probably just cause slight heating, it is still generally a bad idea.
So it is best to keep the charger circuit directly connected to the battery, but isolate the load with a MOSFET, so when charging, the only thing the charging circuit "sees" is the battery.