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Brian,
First if you think of it as drawing a line between the center of the two holes it will give you a better idea of what I am saying.
If the material is large enough to get you the finished diameter you want then in theory it doesn't matter, the the following considerations.
Having the holes as close to center as possible allows you to use a smaller piece of stock and therefore requires less machining.
When the holes are not centered you will most likely end up, for a period of time, making and interupted cut on one end untill the stock is cut enough to make the holes on center. This can cause additional strain on the equipment and cutter and you have to watch to make sure the vibration from the interupted cut does not loosen things up. If the material is thin it can cause it to bend slightly so you want to take lighter cuts until you get past this point.
One thing to keep in mind is if the part is overly large in diameter turning it in the lathe when it is too far off center is like having a tire out of balance. The faster you turn it the more vibration you get till it gets to a dangerous point.
Finally it can take longer to bring the stock to size since you will be making a cut on one end till you reduce the diameter enough and the rest of the travel the cutter will not be cutting or only taking very shallow cuts.
On occassioin in the past when I had a hole on one end that was off center and I had enough stock length I would drill the end that was off out about 1/2 its diameter then make a (lets call it for lack of a better term) false center. This would fit snuggly into the hole and then I would use a center drill to redrill the hole closer to the center where it belonged. When done just cut the piece to length and discard it with the false center.
Good luck..
DonT
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