Actually it is stranger than that. I didn't notice the new NCsoft Launcher icon on my Desktop and figured it just redirected the City of Heroes shortcut to the new launcher.
When I run CoH from the old shortcut, I see the new launcher pop up, launches CoH, disappears ("set to Exit Launcher") and then I see the CoH arrow until after I click on the CoH window the cursor disappears; although it exists once I move the cursor to outside of the CoH window.
When I run CoH directly from the new NCsoft Launcher I don't have a problem with the cursor.