Hi Davide,
Yes, the PMIC be supplied from an external source, even if the battery is present and being loaded, use external 5.0V from USB on VBUSIN.
VSYS voltage interact with the battery charge. VSYSMIN parameter sets the point where the VSYS loop starts taking control and regulates the output. 4.3 V is the recommended setting to ensure that there is enough headroom before reaching UVDET.
Check Figure 17 of the datasheet that shows the charging profile for a better understanding of the relationship between VSYS and the battery charge.
Do not connect external source to VSYS.
Regards,
Jose