The idea behind it is to avoid your starting engines and then AT telling you they cant get you away for half an hour. Depending on the aircraft it is a major hassle to shut everything down again (although not so for most of us).
As others have said it therefore really comes down to the airport. At anything reasonably large you will probably have called AT from ops to book out anyway so just ask then if they require a start up call when you are on the 'phone to them.
I suppose if you are not sure it just as easy to ask before, but the worst that can happen if you start without doing so is you call for taxi to be told there will be half an hours delay. Guess you will just shut down again in that case.
(Edited to add having just read the question properly)
I guess you could save yourself a cup of fuel if there are some checks you can get out of the way before startup. For example it is interesting some people start and then sit on the pad fiddling around putting their route into the GPS which if it is complicated make take a while when this could all be done with the engines off.
However on some types (with glass cockpits) watch you dont drain the battery whilst doing so.
Also, you will see plenty of people call for startup and then start with all the avionics still switched on,
and finally in the winter when it is cold running the engine for a while longer on the pad may be no bad thing anyway to bring it up to operating temp.
In short, all down to the circumstances.