What happens to teeth with crowns during teeth whitening?

I broke two of my front teeth in an accident a while ago and had crowns placed to match my natural tooth color. However, my natural teeth have turned yellow and are bothering me, so I would like to get teeth whitening treatment. I have heard that prosthetics such as crowns or inlays do not have a whitening effect.

Has anyone else had teeth whitening done while wearing dental prosthetics like me? I am curious how the procedure is performed when there are crown treatments.