The main fuse box in the engine compartment is where the mother of all NSX fuses, the big ass 120 amp PAL fuse, lives. The alternator (and other important NSX electrical stuff) is connected to the battery through that fuse. In normal life, the rectifier diodes in the alternator are reverse biased by the battery voltage and no current flows when the alternator is not running. When you switched the battery polarity you forward biased those diodes into a dead short resulting in big time current flow (think DC arc welder). If you are lucky the 120 amp fuse popped fast limiting current damage and everything may be fixed by replacing that fuse. Make sure that battery is disconnected during replacement of the 120 amp PAL fuse.
The main EFI relay has internal bias diodes which prevent the ECU or the fuel pump from being energized if the 12 volt polarity is ever reversed - normally caused by trying to jump start the car with the jump start cables reversed. Because of that protection you should not have any damage to the ECU.
Even with the engine cover fully open I cannot get my head in there to get a good visual inspection of the PAL fuses. I think you will have to unbolt the fuse and electrically check with a continuity tester to confirm its status. With respect to all of the other fuses, I have never been able to visually inspect the AT style blade fuses with the fuses in place in the holder. I generally need to remove the fuse to be able to see the fuse element from the side. Even then, checking the resistance with a multimeter is the gold standard.
You will have given your alternator diodes a shot. The fuse is rated at 120 amps; but, it is not a current limiting design. Based upon typical fuse I2*T curves. the fuse will allow up to about 400 amps to flow for about 1 second before it melts. Don't be surprised if your alternator now has an issue or develops issues in the near future.
