Like everyone else said, it's up to you whether or not you want to use a wig or not. Some people use non-permanent hair dye and style their hair like the characters. Although this is a tough option for many reasons being that it can't be great to dye your hair such an un-natural color and the huge mess. I would personally just go with a wig, cheap and easy. I'm aware some wigs can get kind of pricy (You really get what you pay for. If you pay for a $10 wig from Party City, it's gonna look like a Party City wig
. Wear as you pay $35, and it be much better quality and last longer. Totally up to the cosplayer.) Since all of Amu's transformations have relatively the same hair, I think you can get away with just buying a wig that looks like her original hair.  
You could just take out the ponytail if necessary, it'll be covered by the hat anyways.
I think people would recognize you with the wig or not, so it's really up to you.