Dear Steve,
Excellent question! I was wondering if you were going to ask that.
The rule is always the same: "Target well, aim straight at the target, and putt straight at and to the target."
The neck turn is for the purpose of capping off the routine to get the "to" part tuned. So the selection of the target and the aiming of the putter face and setup "at" the target have been done and left behind. The neck turn is concerning the "to," and the straight stroke will follow. So the danger is that the neck turn can still mess up the straightness of the stroke or get you to revisit the target selection or the aiminging of the putter face. Don't let it. Visualizing the ball starting off "at" the target spot but then curving off line towards and into the hole tends to orphan your consciousness of the target spot as a starting diretion ("at") and as stopping place ("to"). Substituting the hole as the main consciousness at this stage of the routine tends to undercut your commitment to putting straight.
The competing "plus" for seeing the ball break into the hole in this visualization is the sense you MAY get of the energy of the putt over its final segment. I have a tip about seeing or imagining this final curve as a NASCAR racetrack banked turn, for which the driver has to get the "speed" thru the curve just right or else he can lose control and hit the wall or go too slow and drop down to the apron and get passed by the pack. So there is a "touch" aspect to visualizing the ball curving into the hole at the end of the putt that is not without benefit. The problem is keeping the benefit without accepting the problems, so the issue is whether you are able to visualize the ball curving into the hole without messing up your commitment to putt straight at and to a target spot or whether you should avoid this curved visualization altogether.
For purposes of making a straight putt, it is best to look only to the "target" spot and not the hole, seeing the ball come to a stop on the spot. But it seems to be an undeniable fact that people will visualize the ball rolling on into the hole over the final piece of curvature. If you do both, just try to remember that you are putting to the spot and not guiding the ball at the end of the putt on a curve (won't happen).
On putts that are pretty straight, this doesn't matter much. And on putts where the separation of the target and the edge of the hole is pretty wide on the ground, this visualizing the ball going into the hole doesn't SEEM to cause a lot of confusion about where the line of the putt is aimed (this is probably an underestimation of the danger). It's just the in-between situations where there is much danger of the targeting for distance by seeing the ball go into the hole over a curve causing problems with the aiming of the putter face and the start line of the stroke. The more definite and committed you are to rolling the ball at and to a spot on the ground as a target, the less danger there is.
Here are suggestions for helping avoid problems or for mitigating the problems.
I always try to see the very spot on the ground, not just sort of aim at a location in the area of the fall line. I try to see the round section of actual grass blades at the real target spot and imagine the golf ball rolling to a stop there AS IF the putt were flat, level and straight without any break.
This brings up the other point. Aiming at the target spot assumes or pretends the putt is flat and level and straight and there will not be any breaking of the ball off the start line. So the real source of confusion when visualizing the ball's roll at real speed for purposes of distance control is this difference between imagination and reality -- the target assumes you stick with the imaginary flat, level, straight surface, but in visualizing a "real" speed roll, the investment in reality tends to bring the contoured surface back into consciousness so that the imaginary roll breaks and curves into the hole. It helps to remind yourself before the neck turn that you are imagining a flat, level, straight putt to the target spot, and then visualize only a straight putt to the target spot, stopping there.
Bottom line: don't sweat it all that much. The difference is usually not that significant. Just remember that you are actually aiming at a spot other than the hole, that you cannot guide the ball over the curve, that you can only putt straight at your target, that so long as you putt "to and not thru" the target that the break will take care of itself, that putting "as if" the ball will roll straight and come to a stop on the target spot is your plan for the correct 'touch" or energy thru the final curve of the putt, and that there is no alternate plan for the putt (either for line or distance). So putt straight with good touch and stop the ball on the target on the imaginary flat, level, and straight surface.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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