Cracks propagate at sharp edges, like corners, and especially at the bottom and ends of cracks. If you drill a hole at the very end of the crack, you make a smooth rounded shape larger than the sharp end of the crack. It doesn't change the stress levels at that point, but because stresses aren't concentrated at the sharp crack tip, the crack doesn't propagate as easily.
Having said that, though, it makes absolutely no sense to drill the holes then obliterate them with weld metal.
Just as it makes no sense to weld over a crack. You may stop a leak for a while, but the stresses that led to the original crack are still there, as is the sharp tip of the crack, and you can be assured it will crack through the weld again.