Other than Ubuntu being utter rubbish, yes it is possible to get by with Linux laptop. As long you don't need it for gaming. Not entirely sure what Zune is, but I am guessing it is something like iTunes for Windows Phone? If so the native music player tends to work, only that you might need to rebuild your catalog. Which might not be an option. Other options to look into are Zune through Vine or Windows VM image.
edit. based on Google running Zune under Virtualbox seems to be the best bet.