The Genesys Logic GL852G hub integrated circuit does not deal with the power supplied by the USB hub to downstream devices. That is handled separately on the USB hub PCB.
Most low-cost USB hub implementations I have seen do not bother to limit the per-port current draw. On such USB hub PCBs, the input 5V power source connects directly to the downward-facing USB connectors.
If you want 4 connected downstream devices to each be able to draw 600mA, your power supply must provide at least approximately 2.5A, and your custom USB hub PCB must be designed to handle that amount of current. You will have to look at the USB hub PCB schematic and layout to decide if that is the case.
The GL852G itself consumes a comparatively small amount of current, see the GL852G datasheet page 30.
The USB standard requires that each downstream port VBUS supply have specified capacitance. Off the top of my head I think it is 120uF. If the USB hub PCB includes the required capacitance, your power supply will see all the capacitors in parallel. You will want to make sure that your power supply can handle that total capacitance.
If you check the schematic, also check the Bill of Materials (BOM). On a custom USB hub for me, I noticed that on the schematic, some capacitor values seemed incorrect. The BOM showed that during manufacturing, the correct capacitors were installed. I had the supplier fix the schematic.