I have a secret push button start in my '04 that I use daily:
http://www.xoutpost.com/x5-e53-forum/21704-cool-push-button-start-all-x5s-3.htm
I'm now convinced that only the models with an automatic starter (where you don't have to keep the key cranked to start the engine, so 4.4i an above) can do this. From the Manual in the section on starting the engine:
X5 4.4i: You BMW is equipped with the convenience starting feature.
The starter acutation continues to operate automatically for a certain period of time and is stopped automatically as soon as the engine has started