In the latest version, if you are updating location every 15 mins and you have no Wifi/3G/Edge connection then ilocalis will cache the GPS locations and then upload them as soon as your phone is re-connected to the internet. As it needs to connect to the ilocalis server for it to tell you where your phone is.
If you have GPS (Location Services) turned off permanently then ilocalis will force it on to check the location and then turn it off again.
So in summary, iLocalis needs the internet to execute the commands and relay back the information, however you can execute most of them via text/sms if using an iPhone rather than an Ipod Touch.