Can I edit the same Pages document on both my iPad and my Mac?
No, downloading it from iCloud won't create a copy. All of your changes will be synced back to iCloud from both devices, and conflicts will be dealt with appropriately (a dialog to you).

As long as both the Mac and the iPad are connected to the same iCloud account, you will be presented with a list of your documents whenever you start Pages on either your Mac or your iPad.