Well, it kind of depends...
If you added too much rum too early in the process, you would kill the yeast. You could be left with something a tad sweet, but maybe too much rum.
If you added it later, the cider will have had a chance to ferment out all the way, and adding the rum could help stablize it.
My husband recently made a bourbon barrel porter... he soaked some oak cubes in bourbon, then added it all to his porter. Thing was, his porter really wasn't ready, and it kind of quit fermenting. I'm not even sure it will carb.