Yes and no.
Your cpu cooler fan needs to be plugged into the motherboard 4 pin cpu fan header. If the fan is a 4 pin PWM fan with a smallish 4 pin lead, then it will be controlled by the motherboard.
If the cpu fan has only 3 pins, then it will be speed sensed by the motherboard, but will run at full speed. The cpu fan header must be connected or the motherboard will shut down.
Other case fans may have either 3 pin connectors, or 4 pin (largish) molex connectors. Sometimes, you get both types). Either can be used. 3 pin fans plugged into three pin headers can be controlled by the motherboard, or by software like speedfan.
4 pin fans with molex(bigish) connectors are connected to the psu molex leads. They will run at full speed. They can have the speed reduced by voltage reduction.
Ultimately, save the cpu rfan requirement, the rest is not that imprtant.