Yes it can, this function is the Memory function, that mean, when you switch off the swich the fan record the last functions used. When you switch on the switch, the fan give you back thoses function. 

The fan was in Winter mode, speed 3, it come again in winter mode speed 3 .. 

There is more then that, here we talk about fan without light, but some fans, like Klassfan, have memorys in the light and the fan, so if the fan is on or off.. Deep then that, if the light have 3 tones, and the power of the light is dimmable, the fan record all thoses datas, to restitutes them for the next start ! 

Same for the Thermostat function and the Hygrostat fonctions. 

Your wall switch become part of your fan ! 

Thank you for this question.