No it wouldn't - the act only tells Johnson what he MUST do. It doesn't prevent him from ringing Macron and saying "Don't agree to the extension request when I ask for it.".
Colluding with a foreign power to act against the wishes of Britain's sovereign Parliament, is it? There's a word for that.
Of course if such a thing did happen Parliament can quickly vote through a revocation of Article 50 before setting up the judicial review and public inquiry...