Except for reducing the overall resistance, I don't think that it would really make a difference. 32 AWG Kanthal A-1 is rated at 14 ohms per foot.
Braided as you have it, it would be 14 ohms per yard, or 4.666666 ohms per foot. That means to get a 2 ohm coil you'll need about 5.5 inches of that wound into your coil chamber. That might be a bit rough. Though I'm assuming that you're doing this because you want low resistance.
The other problem that you might run into is with the way the coil itself works. The more surface area of wick that the wire is touching, the better it will generally vaporize. You don't want too much of the coil touching the air, or you're just sucking on a warmed up wire. The braid -might- work to your advantage because it has nooks and crannies all over to let
juice in, but my gut is telling me that it's going to cause more popping and splattering than actually improve vapor production.