Multi-Cell Lithium battery balancing circuit explanation
Let's start with the VGS ID curve.  Fortunately, the schematic lists the part number for the MOSFET (BS170), so, from the datasheet:



Notice that at 3.0V, the MOSFET is already conducting 50-100mA typically.  Note that 3V is listed as the "maximum" VGS(th), meaning the "typical" threshold voltage is probably somewhat lower.

Let's look at the circuit.  As Marko Bursic's comment points out, it is used for "PWM signal rectification with amplitude doubling".  Applying a PWM square wave excites an AC current passing through C5.  When the current is positive (to the right), D7 conducts, charging the parasitic gate capacitance Cgs of the MOSFET.  When the current is negative (to the left), D8 conducts instead, preventing the negative current from discharging Cgs.  Meanwhile, R1 is constantly discharging Cgs, and as soon as the PWM waveform is turned off, Vgs will begin decaying and the MOSFET will eventually turn off.

But wait!  What happened to the "voltage doubling"?  Well, it turns out that a "voltage doubler" produces a DC value that is 2X the peak value of an AC waveform.  In our example, the AC waveform is 3.3V peak to peak, or 1.65V peak.  Which means the "doubled" voltage is still just 3.3V, less the diode drop.

So in conclusion, it is theoretically possible that a worst case combination of high diode drop and high VGS(th) could prevent a certain channel of this circuit from working.  If the circuit is intended to work with 3.3V PWM, you're probably fine as the designer probably tested quite a few of these.  If the designer tested with 5V PWM instead, you may eventually hit a problem - but my guess is, you'll still be fine.

Quick aside: "PWM" typically implies that the duty cycle of the signal is a control input - that's not the case here.  The current through the MOSFET is totally independent of duty cycle!  The only purpose of the so-called PWM is to produce an AC waveform.