The answer is Yes. Or no. Or sometimes.
Well sorry, but you will have to read the TOS or license agreement on the stock photography website. Because there are stock photo website where you as webmaster can get a license that allows you to use the photo on the clients site and there are stock photo websites where the client has to create his own account and there are stock photo websites where you are not allowed to alter the image and there are stock photo websites where you can modify the image to death and there are even stock photo websites where you can choose from different licenses.