It was very much real, lots of effort was spent to make sure everything worked correctly, especially around older billing systems which used only 2-digit years in fixed width records.

Because of all the preparation and upgrades being done, I think only incident we had when Y2k migration manager sent out "all clear"-email after rollover - Unix mail client he used formatted date on email as "01/01/19100" - though I suspect he knew of the issue and didn't upgrade on purpose just to make a point.