You can do anything you want, you just can't expect to be free of the consequences when you do.
Track/race tires are directional for a reason. They're constucted and designed to run in one direction. Just because you can do something doesn't mean you should.
You can play basketball in flip flops if you want, but I don't recommend it.
It cracks me up the way people spend thousands upon thousands of dollars to risk their lives on the track, but won't put on fresh tires.
It's like people who live in a mansion, but eat out of the garbage can to save money.
Flipping race tires can result in "catastrophic failure" not to mention, totally different grip characteristics. If the rear fails, you might save it. When the front fails, you're done.
Think Stephen King's "Pet Cemetary" Some things just aren't meant to come back to life, no matter how much you want them to.