Whispernet is Amazon-speak for their wireless (3G or WiFi) network. Whispersync is for syncing your spot on multiple devices. So, yes, you can turn off Whispersync, but still have access to Whispernet for wireless shopping or delivery of books.
You turn off Whispersync by logging onto your Amazon account and going to the "manage my kindle" page and scrolling down to the bottom of the page. It should have a line saying "manage device synchronization". That page should explain a lot better what I've been trying to say
(or what Tiersten said, only faster!)