This will work fine, assuming the connection to the case is for PWM control. The additional power required to run the fans/leds is provided by the sync controller's sata power connector so you have no risk of overloading.
Thanks for putting this together I gave it a test and the LED control worked great but it's unable to detect my cpu (threadripper 1920x) temp so fans are stuck at 100% speed even setting them to manual: I'd be super happy to test/troubleshoot more if requested, even with just manual fan adjustment i'd use this over the TT software.
Are you connecting the Sync Controller via just one PWM cable? There's a PWM port next to each of the groups of three fan ports, maybe they offer pwm control for only the fans next to them.