No. They will not create value. They will take tax payers money and build an inefficient mining operation that even can harm environment and wastes energy. 
When the government runs something it is always inefficient. Any other business would go bankrupt if they spend 2 dollar to earn 1. But if it is taxpayers money they can even spend more to earn less.

Yeah, let them mine it,
and maybe this time they’ll actually create value instead of just printing it