No. Sorry. Explanation follows.
Currently there are two dominant forms of lighting devices on the market. "Lighting devices" can include light strips, lighted fans. etc. Recognize that a lighted fan is really two devices in one unit - a fan motor, and a set of lights mounted in the frame - and the two are powered and controlled completely separately, so they have separate cables. The plain RGB lighting system uses a 4-pin connector (lighting device has a female connector with 4 holes) supplying a common +12 VDC power line and three Ground lines, one for each of the three colours (Red, Green, Blue) of LED's in the device. Along the strip all of the LED's of the same colour (say, Red) are connected to the Ground line for that colour, and so on for the other two colours. The lighting Controller (e.g, a 4-pin male header on the mobo, OR a separate third-party box) manipulates each of the Ground lines to change the colours, so it can change brightness, colour, and the speed of changes this way. But at any moment the entire light strip is all the same colour. In this system, each connector has the pin (or hole) on one end marked, and this is the +12 VDC line. At every connection point you MUST align those.
The more complex Addressable RGB (or ADDR RGB or ARGB or Digital RGB) system uses a 3-pin connector (looks like the 4-pin one with one pin missing from a blank space) that contains common +5 VDC and Ground lines and a Control Line. Along the strip the LED's are divided into Nodes. Each Node contains one LED of each of the three colours plus a Control chip. That chip listens to the Control Line and responds only to instruction packets addressed to it by manipulating only its three LED's. Thus at any moment every Node along the strip can display a different colour, and the display patterns can be much more complex. Because the connector pin arrangement is (4-1), there is only one way to make a connection between cables, etc.
Because the supply voltages and methods of display control are so different between these two designs, you cannot mix them in the same circuit. Your case came with the ADDR RGB type of lights in the fan frames. You say your mobo has only the 4-pin plain RGB type of header. So you cannot connect from that to the lighting control system included in your case. But, you have not told us exactly which MSI X470 mobo you have - there are several. On their mobo line MSI uses the labels JRGB for a plain RGB header, and JRAINBOW for an ADDR RGB header. So look closely for that latter type with 3 pins in case you have one without having noticed. Assuming you do not, your best option is to ignore any attempt to connect to your mobo. Just use the LIGHTING Hub to connect the case lights (and fan lighting cables), and then use the battery-powered hand-held control box to make manual selections of light displays. That control box offers a lot of choices.
You have not asked anything about FAN MOTOR power and control, so I have not posted anything about that here.