I’ll say “no.”
The common argument for “yes” confuses absolute and comparative advantage. If you can see that conclusion right away, I commend your economic intuition. Eric Rasmusen unpacks the core insight:
The naive view is that if Canada has lower productivity in all its industries than the US, then if trade opens up, Canada will produce nothing, and will instead import everything from the US. The fallacy in this is that if Canada produces nothing, it will have nothing to export to the US, and the American sellers will not send anything to Canada. What actually would happen is that Canada would import from the US the goods it has the biggest productivity disadvantage in, and export to the US the goods for which it has the smallest productivity disadvantage. Free trade will benefit some Canadian producers, despite the fact that their productivity is lower than that of their American counterparts.
It would also be true that even if Canada has onerous regulations that hurt its productivity, Canada would benefit from opening up trade with the US. It would actually become easier for Canada to maintain its welfare state, because the country would become richer.
Here is more:
Suppose we have two countries, one and only one of which imposes costly regulations on all its industries– a family leave law, or a minimum of 6 weeks of vacation, or something like that. Let’s call them Canada and America. Initially, the countries do not trade, because of prohibitive tariffs. Then we drop the tariffs. What will happen?
In this situation, nothing will happen that is any different from the opening of free trade between any two countries. Each country has a comparative advantage in one or more goods, and will export those goods and import the others. If Canada’s onerous regulations are equally onerous for all Canadian industries, the regulations will have no effect on trade patterns. Instead, it will be the same sort of effect as if Canadian labor productivity were 10% lower than US productivity. Whether lower productivity is because of regulations, taxes, or anything else doesn’t matter.
More weight on the scale: Trade is a substitute for factor migration. The more a welfare state country trades, the less likely it is to lose factors of production. And the richer the country it becomes, the more likely it can afford higher levels of taxation. It is because of free trade, in part, that today’s world can invest so much in welfare states.
That being said, I am less convinced that very high levels of immigration make it easier to have a welfare state. In this regard trade and migration are not perfect substitutes, especially once politics enters the equation.