What if the Continental Army was successful with their invasion of Quebec and how would they achieve this victory? What would be the effects of this victory?
Are we talking Arnold's expedition to Quebec in 1775/76? If we are, it was doomed from the start. Even
had Arnold's men succeeded in their desperate attack in December, they would have rapidly found themselves besieged and either driven from the city or captured when Burgoyne's 9,000 men appeared in the spring. The Patriot forces simply lacked the ability to project power into Quebec and/or hold the territory they had taken. The fact that General Wooster spectacularly screwed up the occupation of Montreal didn't help either.
If the Patriots made another go at it in 1780 with more men, maybe there was a chance of success. Considering the need for resources on other fronts though, I'm skeptical.