Suppose say, I have a training set of RGB images all with a bit-depth of 8. I pass those images into a CNN and I get a training set accuracy of 'X'.
Now, I take those same images bit with a bit-depth of 16 and 32 and pass it through the same network and train the network again from scratch. Will there be any changes in 'X'?
Does the extra available information in the images have any impact of the CNN?
Higher the bit-depth, more information your image is supposed to contain.
So if you are converting your 32 or 16 bit images to 8 bit images you are losing information. That means you are throwing away some information that might lead to a decrease in your model's accuracy.
But, this is not always the case. It depends on your data and the kind of patterns you want your model to learn. It might also be the case that your model doesn't need that extra information and is able to generalize to the 8-bit images better than the higher bit depth images. So may be you can save some processing time and memory by using 8-bit depth images.
Having no information about your dataset distribution, I can only suggest you to train your model on all bit-depths and then see yourself which one works the best.