LTC4065L connection to active circuit

We're curious on how the LTC4065L performs in the following situation, and what the recommended design is.

There's a battery connected to LTC4065L, a 5V input to the LTC4065 and a circuit connected to the battery as well. See the attached diagram.

If I have understood this correctly, during charging, some of the charge current will go to BAT1 and some to U2. However, LTC4065L will have no way to determine this, and if U2 constantly draws a current >1.9mA (1/10 of the charge current), LTC4065L will never detect a fully charged battery. Further, the expected time to charge BAT1 will depend on how much of the programmed current U2 draws. Is this correct?

Further question; how would one design a circuit with the LTC4065L where the battery is in integrated into the product and therefore cannot be disconnected during charging? It is important that U2 receives no power dips as this can cause a restart (I figure some ripple that can be suppressed with capacitors is OK). Any pointers or reference designs would be much appreciated!