Hardware-wise it might work. looking at the ATmega32u4 datasheet. It seems the connection is a regular serial port, so you should be able to change this in the code. Please see MultiWii forum for instructions on that. I can't tell from the NanoWii pictures if the special connector for Spektrum is on there, but if it is, you'd have to find the other (TX from board) connection as Spektrum only uses 3 wires (VCC, Signal/TX from satellite to RX from board, GND) and you need 4 for GPS (VCC, TX, RX, GND).
Regarding software I can't say anything about the code not fitting on 32u4... There's a special section in the code for ProMicro, Leonardo and 32u4 (last two are the same I believe?).
M4d_D: Please look into the config.h for your GPS settings, it's all there
The green light on my board always lights up if powered on. So there might be a connection issue? BTW GPS_FIX LED doesn't work standard (see couple of pages back). I use beeper to confirm GPS_FIX (beeps like crazy if not fixed to GPS when switched on).