I used to cut weight with a wet suit. I would take off in 0-15 degrees Fahrenheit and run a few miles. The sweat pours after a few minutes of exercise. The practice is illegal in Minnesota.
Just a vest seems better, and probably worth a shot. Worst case the sweat pours down into your pants, I'm sure it's not dangerous. Not sure I would try it in a race setting the first time.
Do you get locked up for running in a wet suit?