lol .....
Not likely in this case, but a good point nontheless.
On a low voltage fan the crossing the hot and return will simply make the fan run backwards. The 3rd wire is a sensor, and shorting it will have no ill effects.
BUT THE VERY GOOD POINT is that before we give advice, especially electrical advice ....
GET IT RIGHT
ps .... PC fans often have Red, Black and a third wire. In this instance, black is the return and red is hot ... but it's 12V, not 120V. Kinda doesn't matter because polarity only controls fan direction, and either can be used depending on circumstances.