There's no evidence whatsoever to suggest that they did, and given the adoption of the practice of royal incest by the Ptolemids (and their general disdain of the native population) it's extremely unlikely. However, Egypt is a hot, sunny place, and even though a royal lady like Cleopatra would undoubtedly be sheltered from the sun as much as possible, it's almost certain that she'd be more tan than many Mediterranean northerners

I think the point of it was that she actually looked more like Cleopatra than our modern interpretations. Modern lore, be it from Shakespeare or Liz Taylor (not sure personally) paint Cleopatra as a stunning beauty which images from the time clearly do not. She was known to have a pronounced nose and was more adored for her charm than physical beauty. You can see this in both bust form (statue is thought to be Cleopatra Philopator, not 100%) and [coin] (http://images6.fanpop.com/image/photos/37400000/Cleopatra-Coin-ancient-egypt-37472819-300-285.jpg).

There is always the case that her name has simply been trashed through history, as could potentially be said for her late lover Marcus Antonius. I think the coinage though is telling evidence.

This is a video reconstruction of what she could have looked like. Skin color is an interesting question as Greeks / Macedonians tended to display themselves as pale, though today they are not, at least compared to other Europeans. Given the lack of photographic evidence and massive displacement of peoples in the last 2000 years its tough to know 100%.