No it cannot work. Biggest problem is that a USB2 standard port can supply 5 VDC power at up to 0.5A, whereas RGB lighting systems use much more current - typical RGB header capacity is 3.0 A.
THEN there's the control issue. This case appears to include lighitng devices of the ADDR RGB type. In those lighting "strips" or whatever, all the LED's are grouped into "nodes" along their length. Each node consists of one LED each of the three colours - Red, Green, Blue - plus a small controller chip for that group only. Each controller chip along the strip listens for an instruction arriving in an addressed data packet coming along the Control Line, and activates its own LED group in response only to an instruction addressed to that node. That system uses three electrical lines: +5 VDC and Ground for power, plus the Control Line carrying the instruction packets. With no instruction packets coming from some microprocessor in a controller, the light strip will only display a single coloiu at all times, even IF the power lines provide all the power required. So you NEED a Controller to get the lights to work! The case provides that and uses a manual button on the top to change what the lights display, exactly for your situation where there is no other Controller available on your mobo. So check the case manual and look carefully for how you connect the ARGB controller module in it to the front top switch used for control. Likewise, look for how that board gets power, perhaps from a connection to a PSU output.