No. As you know, there are two main designs of fan. The older one uses THREE pins, and its speed is controlled only by changing the VOLTAGE supplied to it on Pin #2. The new design uses FOUR pins; its voltage supplied on Pin #2 is always 12 VDC, and it gets the new PWM signal from Pin #4. Inside the 4-pin fan case there's a small chip that uses that PWM signal to modify the flow of current from the 12 VDC line through the motor windings, thus altering its speed. If you plug a 3-pin fan into a 4-pin mobo header that is actually using the new PWM Mode of control, that fan gets the constant full 12 VDC from Pin #2, and does NOT receive the PWM signal from Pin #4 - BUT it could not use that signal, anyway, because it has no special chip. So it runs full speed all the time.
Almost any fan HUB gets all the power for the fans plugged into it via a cable that must plug into a SATA or 4-pin Molex output from the PSU, and it sends that out to all its fans on Pin #2, just as a mobo header would do. But the Hub actually draws no power from the mobo header, so it is not limited by the power output of the header. It does get the PWM signal from the host header and shares that out to all its fans. So a HUB only works IF it gets a PWM signal to share, AND if all of its fans are the 4-pin type.
To connect several fans to a single mobo header, you must use a SPLITTER, which is a different device. It has one input "arm" from a mobo header, and two or more output "arms" to plug in fans, and NO arm to connect to the PSU. So it can only supply to all its fans together the max rating of the header, which is 1.0 A. It does NOT matter whether the Splitter is made for 3-pin fans or 4-pin ones; it will work with both types. Further, the mobo header it is connected to, whether it has 3 pins or 4, MUST be configured in BIOS Setup to use the older Voltage Control Mode (aka DC Mode), not the new PWM Mode. Here's an example of a 2-pack of 4-pin Splitters with three output "arms" each.
https://www.amazon.com/Splitter-Com...1&keywords=fan+splitter&qid=1611887723&sr=8-4
You are buying one fan. I presume you have more that that. So the first point in adding to your current fan group is that it is MUCH easier to connect several fans to a single mobo header if they are all of the same type. So, are your old fans the 3-pin or 4-pin type? IF they are all 3-pin ones, you should be using a SPLITTER, and the max current limit will apply. We can help with that if you tell us exactly what fans you have. But if your old fans are of the 4-pin design, then DO buy a new FOUR-pin fan and also get a HUB that works with that fan type.
A last note. the 3-pin fan you linked to has two connectors on the end of its wires: one standard 3-jole female fan connector, and one male 4-pin male Molex connector. The intent is you use only ONE of those to power the fan. Use the small connector to plug into a mobo fan header or Splitter, OR use the wide connector to plug into a female 4-pin Molex output from the PSU. But NEVER connect both!