It seems to me that Apple would not have announced in their keynote the 4/24 date if they didn't have enough manufactured stock to fill initial demand.
Now, granted, it does appear that stock is not meeting demand.
However, that being said, it does appear that there is enough stock on hand to get the watch into many of the hands of those that were successful enough to be in the first wave of order dates.
It's not like Apple only has a couple hundred of these watches made. They have thousands that have been in production for months. It's just unfortunate that they could not keep up with demand. Same thing happened with iPhone 6, though on a lesser scale. However, in that case, Apple still delivered ahead of scheduled arrival dates.