Probably will work. Three items for you to know so you can verify.
You use the term "LED Fan". What that term means is a fan that has some LED's (normally of only ONE colour) in the frame that are simply connected in parallel with the fan motor so that they share the motor's power supply from the mobo header. Such a fan has only ONE cable from it ending in a common 3-pin or 4-pin female fan connector. The new RGB Fans comes in two different versions, but they have two common characteristics: they have multiple colours in them that can be changed by a controller over time, and the unit has TWO separate cables - one for the fan motor, and one for the RGB lighting system. I'm going to assume you do have the "LED Fan" type.
You can always replace a plain fan with an LED Fan and it will work, because the added LE$D's merely are connected to the same power line as the motor. When you do this there are two small cautions. One is the the added LED's use some more current - a common fan might use up to 0.20 A, but an LED fan can use 0.35 A. This becomes an issue uf you try to connect several of them to a single mobo fan header using a Splitter, because the fan header can only supply up to 1.0 A total. So you must check this limit when doing that. However, in your case you are going to connect to a case-mounted fan speed system, not to a mobo header. And that system appears to draw power from the PSU through a simple two-speed switch, so I expect it can deal with the small increase in amperage from the change you plan. Further, I expect that it really does not matter whether the fans you have already and the new fans you plan to repalce them with are 3-pin or 4-pin models
Lastly, you will have no control of the lighting effects. The LED's share whatever power is supplied to the motor. The speed control switch on your case sends either full 12 VDC or some reduced voltage (about 6 to 7 Volts, probably) to the fan. That MAY mean the the light will be a little dimmer when you chose to run the fans at slow speed, but I do not expect they will ever turn off unless you can turn the fan off completely.