No, there is no way to connect an ARGB lighting system to a plain RGB controller and header. The two systems are very different in voltage supplied and control methods. The other option for some systems is to connect them to a mobo ARGB header (of which you have two, both in use). But you may have no way to do that, either.
The 3-fan kit you got also contains their Lighting Node Pro controller box. It is intended for use without any mobo header, and it is its own controller. It gets power from a connection to a SATA power output from the PSU, and it communicates with the mobo via a cable that connects to a mobo USB2 header. In turn, the iCue software you download and run uses that connection to send control signals to the Node, and hence to the lights in the fan frames. This all happens completely independent of whatever Aura Sync is doing via its mobo ARGB headers.
There are SOME such systems that allow a third cable connection from the proprietary light control box to a mobo ARGB header, and a way to tell the proprietary box to stop doing its own thing and do whatever the mobo header says. In that way you can get ALL of your ARGB lights to do the same thing, but you lose any special lighting patterns the proprietary box knows how to do. As far as I can tell, this option does NOT exist for the Corsair iCue Node box. The only way to control lights with it is to use the iCue software and its capabilities, and you cannot sync those light displays with others supplied from the mobo headers.
IF you really want the fan lights to do exactly what the mobo-connected lights do, the only way would be to rig a connection to those fan lights from one of your mobo headers instead of from the iCue Node box. That certainly means finding out the right connections to make and custom modifying the Corsair wiring to achieve that. Then you would need one or more ARGB Splitters to enable you to connect more than one light system to each of your two headers. BUT it also means you MUST consider the limits of the mobo headers. They are spec'd to supply up to 3.0 A max current to the load (from each of your two ARGB headers). The problem here is that means you need the specs for the LIGHTS of each fan, plus for the lights you already have connected to those two headers. The Corsair website for those fans specifies the FAN MOTOR max load, but does not tell you the LIGHTING unit loads for each fan. I don't know if you have the current data for the light strips you already have. Unless you can get those data and ensure you do not overload the mobo headers, do not so this.