What matters with synthetic fibers is more about drum rhythm
Although it is true that typically the wash rhythm is gentler for the "synthetic" cycle than for the "cotton" cycle, I am not sure this is what matters the most.
The main characteristic of "synthetic" cycles is to prevent sudden changes of temperature, which would "set" the wrinkles.
Typically, if the wash temperature is above 40 °C (104°F) at the end of the wash, cold water is added to cool down before draining so that when cold water is used for the rinse there is no thermal shock.