Yes, but each type of color film will require different development times just like different B&W film. You should test for best results.
Remember, when you photograph using color film, you are actually shooting B&W. The color is added later in the development process.
Color film has three layers of B&W emulsion, each sensitive to different parts of the spectrum (to say it simplistically — since all three layers are sensitive to the blue spectrum, thus the reason for the yellow filter built-in to the emulsion to separate the red and green layers from the blue).
Shoot, develop, and have fun to your hearts content.