In order to answer this question, you need to have a good understanding of how the eye and brain communicate and perceive color, a simple understanding of light, and good definitions of "colorless" and "invisible".
So first, I'll try to define invisible and colorless, and what the difference is. In normal, everyday talking, "colorless" means something that is left uncolored, however this is not what we are using it for, and in this context it means a state of absolutely no color. "Invisible" on the other hand, means something is incapable of being seen, or basically hidden.
Now, here is where we have to understand how the human eye works. I recommend the wikipedia page on trichomacy, which basically says that human eyes have 3 separate detectors for color. This means that there are 3 values that the brain has to work with (imagine that there are 3 wires, and each one controls a different color, for example one would tell you how much green there is, another how much blue, and another how much red).
If this seems a bit complex, it's because it is. But what this is telling us is that the eye can only really differentiate between 3 separate colors, and the brain mixes the signal to create a full color image. A black picture has no green, no red, and no blue in it, so this means none of the 3 types of cones are stimulated. A white image has 100% green red and blue in it, so all 3 channels are fully stimulated.
Not all light is "visible", meaning that the human eye is not simulated in any way by it. This means that for trichomats at least, a black signal is the same as an infrared signal.
So, does colorless mean invisible? Colorless and invisibility are two separate things in my mind, as something that is colorless doesn't stimulate our eyes, but it blocks out whatever is behind it, whereas something invisible would have to bend light around it in order for us not to see it.