Is there a way to warp an element around a sphere in Illustrator?
Turn the element into a Symbol, then use the Map Artwork function in the 3D dialog to put it onto the sphere. (This assumes you've created the sphere by revolving a circle. Your question doesn't specify.)
Might be more helpful to give an example of the type of element. In these programs you’ll find there’s more than one way to skin a cat.
If it isn’t the effect you wish, look up not only WARP tools, but MESH tools as alternatives.