Big turn of snubber: Yes it does. If it was not present, the drain voltage would rise to a (too) high voltage and probably destroying components. As charge entered the clamp capacitor (that is precharged in previous cycles) shortly after the main switch turns off, it must be "extracted" also, otherwise the clamp capacitor voltage would continue to rise.
The charge is extracted via the primary inductance back to the power supply (as Vclamp is above supply voltage). Of course this requires the clamp fet to be on. When the clamp voltage drops sufficiently, the clamp fet can be turned off. Turning of is ZVS as the current will be taken over by Cdrain.
Theoretically you can use a N-fet and divert the current/energy in the leakage/magnetizing inductance directly to the supply. I tried to draw it simpy, but I couldn't draw it without the need of high side floating driver. The reason is that you use the body diode to turn on automatically when the drain voltage reaches Vsup + Vclamp., so you don't need very strict timing for turning on the N-fet.
So basically, switching loss is the same for both capacitor clamping with N fet or P fet, but P fet is simpler to implement. If you design it well, some remainder of stored energy in the transformer (during that the transformer primary current is negative (so goes upwards) ) can be used to discharge the drain capacitance to below zero to enable ZVS.