OK, now I have more questions. But first, a few "answers".
You say your fans are by Antec and they have 3-pin connectors on them, plus a cable that ends in a 2-position switch for speed control. I have similar Antec fans from some time ago but they 3 possible speeds and have 4-pin Molex connectors on them, so they cannot plug into a mobo fan header. Now, the "standard" 3-pin fan connector is female with 3 holes in a connector about ½" wide, and ridges up one side of it. It fits neatly onto any mobo SYS_FAN or CHA_FAN header, and the groove system ensures it only goes on one way. Is that what you have?
If that is the connector you have, then the speed of these fans is controlled entirely by voltage. Power is fed to the fan on Pin #2 (Red wire) of the connector, with Pin #1 (Black wire) as Ground. For control, the mobo header varies the voltage supplied on Pin #2, from about 5 VDC min up to 12 VDC. The Yellow wire on Pin #3 takes a pulse signal (2 pulses per revolution) generated in the motor back to the mobo header for reading. The mobo does NOT use that speed signal to accomplish control, although often it does monitor that for possible failure of the fan to work. It appears that your fan also has an additional non-standard feature in its special switch on the end of a cable. At the "Low" setting, all that does is insert a resistor into the power supplied from Pin #2 to reduce the voltage going to the fan motor. In its original design, this was the only way to change the speed of these fans, because they were fed from a fixed 12 VDC source from a Molex connector. But when they are used with a mobo fan header that actually does use Voltage Control Mode, you should always leave that fan selector switch set to "High" so that it does nothing to the supply voltage coming from the mobo.
SOME mobos with 4-pin fan headers use only PWM Mode to control fans. That system always supplies the fixed 12 VDC on Pin #2, and then sends the new PWM signal to the fan on Pin #4. Inside the fan is a chip that uses the PWM signal to modify the flow of power from Pin #2 to the motor, thus changing its speed. But a 3-pin fan cannot use that signal, so it can only run full speed if plugged into a true 4-pin fan header using PWM Mode. In that case, the extra switch on your fan could be useful. Just let me alert you about this, though: 4 pins on a fan header do not guarantee use of PWM Mode. There are some 4-pin headers that allow you to select in BIOS Setup which method it will use for fan speed control, and there are also many mobos today that use 4-pin headers but only use Voltage Control Mode (the system for 3-pin fans) on those headers.
IF your fans do have the "standard" 3-pin connector on them with 3 wires coded as above, then very likely your mobo headers CAN read their speeds properly, and hence Corsair Link should be able to display them. In that case, how you set the special added switch on the end of the cable will not interfere with the ability to read speed. BUT it certainly will change the speed, and it might interfere in this way: if you set it to "Low" and the mobo also tries to slow down the fan with a lower voltage, the fan may receive such a low voltage that it stalls. If that happens, the mobo might detect that and raise the voltage to re-start the fan, then lower it again to slow it down. Repeat cycle. THAT is why I said you should only set the switch to "High" if your mobo is actually able to slow the fan down by itself.
Now my questions: since you say that now all those fans are connected to the mobo headers, do their speeds actually change as the system workload changes? Does Corsair Link now display reasonable speed readings for them?
You have a lot of confusion about 3- and 4-pin fans. BOTH types can report their speeds to the mobo. The two types differ in the WAY that their speed is controlled. To do that, the mobo header must use different signals sent out on its pins. And lots of confusion - NOT yours - is caused by the way that mobo makers have used odd designs for their headers' control systems.
Like many makers, Noctua makes both 3-pin and 4-pin fans. They are not all the same.
If you tell us your exact mobo maker and model number, we can look up its fan control system and advise. Tell us also how many case vent fans you have, and tell us about what they are doing now while connected to mobo headers. Also tell us this: are you using any Splitters to connect more than one fan to a single mobo header?