It depends on the Chairmans loyalty i think. Which is a hidden attribute unless you have FM Scout or FMRTE. If he is loyal and/or likes you, then i would imagine he will stick with you. However you can also get a Chairman like Mike Ashley or Abramovich who will sack a manager at the first sign of trouble.
You will have increased your club stature significantly and that means you would be very unlikely to be sacked. I done a similar youth challenge in England and got relegated from the Premier League after already staying up twice and wasn't even under pressure.
You might have some job security issues if you don't meet their expectations which is to avoid relegation. I'd say you would be hard done by but if you have the wrong guy in charge then they may sack you. They will give you definitely until you are relegated, that is if you do go down