No, one of the main problems here is that people also pull on the bit while they neck rein because their horse's are not properly trained or the people don't know how to ride. When you do that, then yes, the signals can get confusing because you are cueing for a left turn with the right rein but also pulling on the right side of the bit and cueing for a right turn. Very confusing, especially to a young horse. So long as the reins are left loose, neck reining in a snaffle is a snap.
Theoretically, the curb bit is used on a "broke" horse that neck reins etc. That's why you can only ride the 5 and under horses in snaffles (at least in the western quarter horse world). Ideally your horse should be completely responsive to the snaffle before you move up to a curb. If you just move up to a harsher bit without addressing the fundamental issues you'll just end up with a hard mouthed horse.
It sounds like your horse could go in either a snaffle or a curb. So it's really up to you. But I would definitely go with a bit that's a little thicker and has shorter shanks if you decide to go with a curb bit.