Can a CNN learn if the inputs have a lot of zeros?

I have images that contain a lot of zero pixel values (25% of the image).

Will these prevent the CNN from learning? Since when the convolutional kernels are convolved with these zero regions, the outputs will be zero after relu activation, and so nothing will get backpropped later on since the error will be multiplied with this 0 value.

Is there a way around this?

It should work fine. The weights relevant to the non zero pixels still learn. MNIST dataset is also sparse and CNN still works very well there.