Garmin Express is not used to upload from the Edge 1000 using WiFi. You do need to initially set up the WiFi on the Edge 1000 using Garmin Express but after it is set up, the device will sync over the network without Garmin Express.
To complete the initial WiFi setup please follow the instructions in this FAQ: How do I configure the Wi-Fi settings on my fitness device?
There are also instructions in the same FAQ for turning the Auto Upload feature on and off.
But can it work the other way around over wifi, much like the iOS app works over bluetooth. So if I am on the Connect website, and a send something to the device, say a segment. Can this go over wifi ? Having to plug the Edge in the computer (I use a Mac) is cumbersome and the sync getting done over wifi would be so much better. I don't seem to be able to do this with my Edge 1000.