Connecting a single-colour LED strip to a RGBW controller
Yes. A RGBW controller is essentially just four individual channels. You can connect a single color strip to the controller as long as it's done the right way (single color negative to the R G B or W, single color positive to the 12V) and the strip is within the single color current limit of the controller. Additionally, you may see a better color from G B or W, as R is often driven at a different frequency to make up for its brightness.