Absolutely. The largest determining factor of migration isn't even enforcement, it's economics. They keep building corporate plantations, bribing local governments, making 'trade' deals with socialist governments in central and south america to import people form those countries (which reduces the burden on the socialist welfare system) and gets them low cost labor.

Start hitting employers with prison sentences and suddenly illegal trafficking will go down.

Now, in fairness, you need to balance that out with allowing for lower wages instead of mandatory healthcare and shit so that people can just get those jobs at a competitive rate, and move on from there.