I have done the blackmail. You get the blackmail choice if you don't get to help Layla study for the Spanish test and you're on her path. You don't get to help Layla if you've hooked up with Lexi and reveal it to Layla at the pizza restaurant instead of at training camp.
Blackmail Gabi speed run does burn all your bridges with her.
I replayed it out of curiosity how it affects Episode 12.
This was a speed run that turned Lexi-Layla relationship paths to friendship paths and burns your bridges in the Gabi path.
You blackmail Gabi for Layla but you're just friends with Layla.
I then focused on Nikki, Erynn, Val, Brooke, Melissa. You can access all the happy Val content in Chapter 12 on this route if you stop pursuing Erynn mid-route. It goes back to @LSC82 confirmed circles theory that you can get all a lady's content if you're on a solo path with them or if you're on a multi-path/scumbag path you can't be with another lady that can block her path.
After the blackmail:
Gabi doesn't even want to make eye contact with you at the restaurant. You miss out on 2 Brooke points by not being able to ask for Ximena's photo (8 points instead of 10, which probably blocks some content later.) Brooke doesn't tell you to watch Ximena's sex scene. You just watch some funny videos on your pc while waiting for John.
But then again Gabi has a right to be done with you. At your worst, the MC was not Ethan level when blackmailing Gabi, but still not the MC's finest moment.
This is a hint at what the MC might have become in the abandoned corruption route for the game.
POOR GABI, BAD MC
NOTE: You can go back up to scumbag level if you just steal the tests and don't blackmail Gabi. The Gabi path will remain open then.