Charge a Lipo battery and power a circuit
Your concern is well-founded. If the battery is connected directly to the system load, there is no way for the charger to know how much current is going to the battery and how much is being used by the system.

For this reason, many chargers isolate VBAT from the system power rail (VSYS). In general, I would say that it is acceptable to put the system load in parallel with the battery when the system current is much smaller than the charge current, OR if the system current is very consistent. In that case, you can just crank up the charge current setting on the charger to account for the system current. But if the system current varies over a wide range, or is not consistent from unit-to-unit, I would look for a different charger IC.

As a side note, it appears that the MCP73831 does not have a charge timer. In other words, the only way for it to terminate charging is when the acceptance of the battery becomes sufficiently low. Normally, state of the art chargers would also have a timer, so that if the battery acceptance never becomes sufficiently low, charge will terminate anyway after allowing a generous interval of time. This lack is even more worrisome since you cannot separate the battery from the system load. The system load will make the battery acceptance appear higher than it really is, and the charger may never terminate, but just float at 4.2 V forever.

I recommend you ask Microchip about this, in case I am mistaken. But if it really is the case, then I have to suggest you look for another charger, because it is not safe to float lithium ion or polymer cells indefinitely at 4.2V. There needs to be a timer so that charge always terminates.

TI uses the term "power path" to describe chargers which keep the battery separate from the system. They are not the only ones with this feature, but I think searching for power path will help you to find chargers that do this, from TI and other vendors.