Yes, that's quite possible. There are a lot of factors here. Nikon DSLR cameras use a CCD sensor while Canon uses a CMOS censor. The software that interprets the information will differ. etc.
It's not really any different than it was in the film days. Different films will give you different colors...even different batches of the same film will give different colors. etc.
Photography is the recording of light...different light sources give off different "colors" of light...also called light temperature.
Sunlight is different from regular incandescent light bulbs. Fluorescent lights are different from either of those.
This is where White Balance comes in.
As Humans, our brains tend to automatically adjust for the different light temperatures we see...but cameras will see the difference. If you take a photo under fluorescent lights...with the daylight setting (on a digital camera)...you will get a strong color cast in the image.
Digital cameras measure the light and try to adjust so that the colors are accurate...unless we override the auto setting. Getting back to the question...different cameras may read the light differently...or they may compensate differently...it's all controlled by the camera's software.