I'm a little confused because the links in the first and third posts are the same. But the answer is YES. I disagree with Shaun O and here's why: That adapter IS cleverly designed to do exactly what it promises. It distributes power and the PWM control signal to all fans, plus feeds ONE fan speed signal back to the mobo port. The "problem" it addresses successfully is that most mobo 4-pin fan ports cannot deliver enough current to power more than two fans simultaneously, especially at start-up time when fan current draw is heaviest. Instead it uses a 4-pin Molex connector as the power source for the three fans, and that source can provide much higher total current as needed. BUT the adapter still provides to each fan the same PWM control signal, so all of them can use it. The circuits located in each 4-pin PWM fan draw very little current from the PWM signal line so there is no real "problem" doing this part. And finally, having only one of the three fans' speed signals sent back to the mobo is the right way. A speed signal is a series of pulses - 2 per revolution - generated by the fan and sent to the mobo for counting. If you feed more than one such pulse train back on the same line, the mobo result will be quite wrong! The only limit by doing it this way is that the other two fans' speeds will never be known, which is OK.
Now, I will point out one thing to recognize as the adapter is installed. If I understand correctly, OP has one CPU fan already connected to the CPU_FAN port on the mobo and that is completely not part of the current discussion. OP then has two existing 4-pin CASE fans operating and wants to add a third in a manner that has ALL of them controlled (speed-wise) by ONE mobo 4-pin SYS_FAN port. This adapter will do that job perfectly. BUT recognize that the connector that goes to the mobo port may be labeled to plug into the "CPU_FAN" port whereas you really want it to plug into that SYS_FAN port. Likewise, ONE of the three outputs is labeled for powering the CPU fan, but should NOT be doing that - OP's CPU fan already is connected as it should be, to the CPU_FAN mobo port. This output is merely connected to one of the three case fans OP wants to use.
Please note: I made an assumption above that may not be correct: that OP really wants to be using 4 fans - one on the CPU cooler connected to the CPU_FAN port, plus three as case fans controlled separately. If, instead, OP means that he / she want to use one CPU fan plus TWO case fans, all controlled by the same mobo 4-pin fan port, that's a different story and is exactly what the adapter is for. You install it exactly as the various wiring labels say. BUT now there is a different limit: the two case fans connected this way will be governed by the CPU's measured internal temperature, and not by the mobo temperature. You need to recognize that most systems have TWO separate temperature measurement and control loops. ONE of them uses a temp sensor built into the CPU and controls cooling of the CPU only (under normal circumstances). The second uses a temp sensor built into the mobo and controls Case Fan(s) to keep the mobo at the right temperature. Using the CPU cooling controller for both jobs is not quite right, although I suppose there is likely to be a reasonably good correlation between CPU temperature and mobo cooling requirements.