NNJZ, fan speed control is NOT connected directly to the fan speed signal normally available on the Yellow line of a 3-pin fan. Here is how fan speed control does work.
For a 3-pin fan, speed is altered by changing the voltage available on the +VDC (red) line. It max is 12 VDC, but it can be reduced by the fan controller system on the mobo that supplies the pinout for the fan. It is what is called a simple proportional feedback controller. It has a target temperature or Setpoint - SP. The actual temperature (or Process Value - PV) is measured by temperature sensor. For a CPU fan (and its controller circuit), the temp sensor is built into the CPU chip case and its signal is fed to the mobo via a pin in the CPU socket. For a case fan the mobo has its own temp sensor built into the mobo and it uses that. In either case, the controller constantly calculates the difference or Deviation (DEV) between Setpoint and Process Value (SP-PV), then multiplies it by a NEGATIVE Gain Factor (hence the term Negative Feedback) and adds an Offset constant value. The resulting number is the Output of the controller that is fed to the Actuator (the fan in this case) that does something to alter the process being controlled (in this case, the temperature being measured). This is a Feedback control loop because the result of the loop's action (changing the fan speed) is measured by the PV (temp) sensor and fed BACK to the controller. It is Negative Feedback because the Gain multiplier is Negative. Why? Well, track the action starting from the assumption that the temperature is already at Setpoint and the fan running at a constant speed set by some voltage output (less than the full 12 VDC max) from the controller. Now, something causes the measured temp to rise - maybe you set the computer to do a big long task. SP has not changed, but the PV rises, and hence the DEV = (SP - PV) goes more negative than it was. Since the Gain is negative also, the product of DEV x Gain is more positive than it was, and the Output will go more positive - in other words, the fan supply voltage increases and the fan speeds up. Likely this will result (a short time later) in a reduction of temperature measured (the PV) and the loop will reduce its output. Over a reasonable time the fan speed will settle down to a new speed, until the temperature changes again due to some other load change. Thus the cooling action is kept proportioned to the need for cooling, and the end target - a constant temperature inside your case - is met. Negative feedback control loops are nice because they actually measure the target parameter and use it to guide the loop's action.
NOTE that the actual fan speed did NOT show up in this control lop at all! That is because the fan's speed is NOT what we are trying to control. It is merely a tool to achieve our real target - constant case temperature. So an actual measurement of fan speed is NOT necessary to operate the fan speed control loop. Now, IF a fan speed signal is available, it is nice to have because it can be displayed for you as information. In some cases, a different control system MAY be used to make sure the fan actually is turning as a safety measure. Some CPU cooler systems add this action and use it as an early warning that CPU cooling may be about to fail and cause a BIG problem, even before the CPU cooling control loop detects an actual drastic rise in CPU measured temperature. But is still is not part of the basic CPU cooling fan control loop.
Bottom line is you CAN control a 3-pin fan's speed from a mobo pinout designed for it, even without a fan speed signal on the Yellow wire. But without that signal you won't be able to see the fan speed displayed.
Of course, 4-pin cooling fans have a very similar control process. The difference is all in what type of Output the controller loop provides to the fan, and what the 4-pin fan can do with that signal.