I have spent 15 years as a machinist and grew up with a heavy mechanical background and following a hole with a drill is a very common and well accepted method of enlarging a hole.

The danger is not in the hole going off center, the danger comes with the type of material being drilled and its thickness, because to do it properly, you can't really hold it in a vise, the piece needs to be free to move - at least for the first few seconds while the drill finds the hole.

The problem is, some materials like plastic can be "Grabby" - likewise with thin material like sheet metal. The drill can auger itself into the part and pull the part (Which is being held down with your hand) up - then the drill can spin the part around and turn your fingers into hamburger.

But with wooden props, I do it all the time (just yesterday in fact). I do it with nylon and composite props too, I'm just a little more careful with them.

And if anyone is wondering about its accuracy, I did a test a few years ago and the hole was less that .0005" (Five - Ten Thousandths of an inch) off from the original hole