Answer: Painting over the bare stems would probably not be good for the plant, it would smother it. But if you pull or cut the ivy off of the building before painting, it should regrow just fine from the roots. It will regrow faster than it grew originally because of the deep, established root system. In the long run, though, I am not sure you will want the ivy growing on the stucco.
I am not sure what will happen when you try to remove it; often the hairy clinging feet remain on the walls because they are so firmly attached. But if the stucco is at all deteriorated behind the ivy, it may come off with the ivy when you try to remove it.
In some cases the ivy is actually protective for the stucco because it keeps rain off of it. In other cases the sheer weight of the plant can pull the stucco off the building; also, the ivy will work its way into any irregularities or cracks and potentially enlarge them.
Unfortunately, I am not sure what the painting professionals would have to say about painting over the hairs left on the wall, but I would think it could be done. You might want to check with the paint supplier, too, and see what their opinion is. Good luck with your painting project.
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