After reading the data sheet I am uncertain if the MCP73833 Charge Management Controller chip is safe to use when connected to the USB, battery and system at once.
The only line in the data sheet mentioning system load that I could find was:
The TE input can be used to disable the timer when the charger is supplying current to charge the battery and power the system load.
This line indicates that it should be ok, but I feel this should be said more explicitly and not in one line that actually is about TE (timer enable) input.
So is this within the intended use of this chip?