Can colored images have more than 3 channel values?
Yes, Images can have more than 3 channels. Satellites routinely record multiple frequencies at once (for instance infrared). Normal monitors can't render that outright and you'll have to project those channels back to RGB. A simple way to do that is false colors.



These three false-color images demonstrate the application of remote sensing in precision agriculture: The left image shows vegetation density and the middle image presence of water (greens / blue for wet soil and red for dry soil). The right image shows where crops are under stress, as is particularly the case in fields 120 and 119 (indicated by red and yellow pixels). These fields were due to be irrigated the following day.

But convolutional nets take inputs (for instance RGB) and transform them to higher dimensional representations by applying several convolutions over the data. That is what you are referring to now. You can think of those bands as different filters that highlight features that we originally detected in the RGB-channels. They live inside the pipeline, and are then projected to a (typically lower dimensional) target (in this case 2)

So You can also input multi-band pictures, convolve those to even more channels.