As an after thought I tested this in Safari on the computer as well. It works, but after the selection you have to be careful to right click on the text, not the link, in order to get the copy option in the contextual menu: That or use the keyboard shortcuts, or Edit menu options.
Hmm, if you use the keyboard shortcut you don't even have to select the normal text. I bet this would work on the iPad too, if you have a bluetooth keyboard connected.