It might be computerized & automated, but I really doubt something like leave status is instantaneous and that you will get detained on the spot, unless you has already been flagged or charged for a military/criminal offence. I say this because from the moment an NSF applies for leave (at least from when I was an NSF), that piece of paper has to pass through a bunch of people... who aren't always the most efficient because they have better things to do than clear your leave quickly for you. Unit clerk > my immediate officer sign/approve > his officer sign/approve > unit clerk > chief clerk > dunno who else > then keyed into the 'system'. Will definitely take some time for it to reflect actual leave status?
E.g., If an NSF on MC decides to cross the border to JB for lunch, I think he'll likely pass through and back with no issue as the assumption at that point is that he has not done anything wrong (yet), could be on actual leave but not reflected in the system yet? That said, it's likely that an NSman who tries to leave the country while he is supposed to be on annual ICT, to be stopped and arrested at the checkpoint because his reservist period would have been updated in the system for at least 6 months.
Anyway, just pure speculation on my part. You could be right and the SAF is really that efficient these days ;p