Even that depends. Supervision or line training is still training. It doesn't really fulfill any unexperienced-roster prevention scheme.
Back when i was fresh out of supervision (around 2 months of line training, other companies do as much as 8 months) i still wasn't allowed to fly with inexperienced captains (less than 1000h on position and type) until i had 500 hours done after line training. It makes rostering a bit more complicated, but increases the overall experience level.