Hi Markus,
The BGATE driver will toggle the FET connecting pack to Vsys. Looking into MP2760 for instance. You are not wrong in your understanding.
Vsys min is the absolute minimum the device will regulate down to as the battery is depleted. However, without NVDC as the battery charges up, there is a +delta of Vtrack where Vsys will rise in parallel with Vbatt.
Another recommendation I have and would like you to have a look is MP2723A. It is a buck charger. However, it is possibly a better fit for your application.
Kind Regards,
Nouman