I could only get past the first level on the VC version without saving. xD But yeah, after looking it up, most people are saying that it will save.
You know how Nintendo always incorporates the star feature of its system, right? Like how the touch screen was all great back in the day of the first DS. Well, do you think they're gonna go above and beyond with a game that makes heavy use (to the point where it's mandatory) of the 3D effect?