It is not going to happen.
Here, the opposition to the Gazoduq project is strong. In September 2019, half a million people marched through the streets of Montreal to denounce climate change, fossil fuels and Gazoduq. To date, BAPE has received an unprecedented 3,000 briefs on this subject; the vast majority of these expressed either outright opposition or asked pointed questions about the so-called environmental benefits of the project. (source)
No provincial government with roughly 4 million of voters (number of people who actually vote, not the number of registered voters) would risk alienating the 500,000 people who marched and the millions who oppose the project.
BAPE and big regulatory hurdles
BAPE is the Bureau for Environmental Assessment and it has final say on any large projects. BAPE has a very good project of opposing bad projects and of standing up to the Government.
Gazoduq Quebec LNG Project Facing Big Regulatory Hurdles as Assessments Begin. The list of approval requirements alone fills a 183-page instruction manual for hearings by a combined panel of the Impact Assessment Agency of Canada (IAAC) and the Bureau d’audiences publiques sur l’environnement du Québec (BAPE).
Billionaire Warren Buffet withdrew his money from the project in March 2020. Effectively killing any chance the project has to find a new financier. (Source)