CNNs for identifying scattered object?
This should not be a problem, the convolutional kernels will have bigger and bigger receptive fields when you get deeper, and either there will be kernels at the end that will combine all the components over the whole input if the receptive field is big enough, or if you use a fully connected layer at the end it will learn that specific combinations of components combine into a specific class. The number of pieces it will be able to recognize depends on the expressiveness of your network, the amount of training samples and on the difficulty of your problem.