This would require some serious scripting power. I've made the enemies in my game "not react to the player" if the player turned the lights off on them and snuck around in the dark... would be the same concept.
I think your real problem here is how to make the person behind the screen not see the character they are using.
Once you can get that then you'll be free to script into the enemies to not react to the player when the player turns on the invisiblility.
The way I did it, is kinda going to remain a secret until the end of the PGPS compo.
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Dammit, Jim! I'm a programmer not a graphic designer!!!
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