Well, I recently found out the answer by testing it in my own kitchen. Now, the results may not be surprising: what you get is a big, buttery glob of chocolaty goo. I experimented a little bit more, by adding some heavy cream and whisking vigorously before scrambling, and while I wasn't able to avoid the ugly factor, at least this version had a little more substance and shape. The taste of the eggs is not exceptional on its own (it tastes like a Creme Egg melted in butter and cream), but it's rather good when put on top of "potatoes" made from diced day-old doughnuts that have been fried in butter and "toast with jam" made from pound cake.
Conclusion? In the future I may stick to regular eggs for scrambling—but it was a valuable lesson to learn that melted Cadbury Creme Eggs taste delicious on top of pound cake!