Yes, the email address can be kept open, but it will need to be attached to an Internet login. The lowest priced Internet account we have is dial up which is $20.45 a month (or $10.45 if you also have home phone and tolls with Vodafone). More info here http://www.vodafone.co.nz/internet/dial-up/
If you don't mind can I ask why you're wanting to switch ISPs? We launched a few new plans recently so might have something to better suit.