Hi- yes, ignoring U2, operation is safe with 5V on the battery input, including R8(1M resistor will pull up to the internal protection diode on AD4). With U2 in place, you should not have problems(it's above 4.2V, so it will not try to charge, but below 6V so it shouldn't cause damage), but the datasheet does not specify operation for this condition(5v on VBAT) so it would be safest to remove it.
Thanks,
Ben