Yes, exactly. With load sharing no load current ever goes through the charger, so there's no issue with charge termination being prevented by excess load current. Also, without load sharing, when the battery becomes fully charged, the charger terminates, so the battery has to take over even though input power is still available. Load sharing prevents that battery cycling.
Yes, but they also say it has protection, which I don't think is true. So I kinda don't want to rely on what they say.
Well, I think the parts I circled in the picture look a lot like the standard load sharing circuit. You have diode D5, which appears to be an SS35 schottky, connecting the USB power to the output, which is also the source pin of Q4 if it's a P-channel mosfet. Then you have the drain of Q4 connected to pin 5 of U1, which is the BAT pin if it's a TP4056 lookalike. And finally you have a resistor connected to the gate of Q4 and to what might be ground. What's missing is a connection from USB power to the gate, but that could be covered up or on the other side, or it could be through the other resistor R5 which IS connected to USB power. To me this looks a lot like this circuit:
