I know the game doesn't really say if they do, but then again there's a lot of things the game straight up doesn't tell you. Does anyone know if they do or don't? Maybe it says in the strategy guide or something?

There are some costumes, namely the different colored ones you get from the VR missions, that will tell you about what special effects they have. I've heard unconfirmed reports that the Desperado color scheme makes enemies take slightly longer to notice you/become alert after seeing you, which makes sense, but I wouldn't be surprised if there were more that just weren't apparent.

Wearing the Mariachi outfit increases the game's awesomeness by another 63%, that much I know.

Yes, they do.

If you play Justin Timberlake "Suit&Tie" while wearing the suit outfit it ups your coolness 120%