Can iBeacons work directly with remote servers?
An iBeacon can't communicate directly with a remote server. iBeacons are low-energy bluetooth devices that only performs a broadcast of it's UUID (unique user identifier), a major and minor numbers. 

On your iOS app using CoreLocation framework you can intercept this broadcasted signal and use it as you please. An example of this is GeoHopper app that has easy integration with web hooks of your choice. You will also be able to get the proximity of the iBeacon device within your app, the proximity is given in four values: Unknown, Far, Near and Immediate.

The video What is new in Core Location (Apple developer account required) has a good introduction to the iBeacon technology.