Sure that seems unlikely, but when millions of people are willing to become undocumented immigrants, it’s likely a more open policy would see dramatically larger influxes. Especially in response to local events like civil wars. Really, just raising the caps by say 10% every year gets the same result without the chaos.
Yeah, I was thinking the same thing when I was writing the above, but didn't want to get too into the weeds on what I wanted to be a short answer to the original question (I have a habit of going on...).
Like many things, an immediate large change has repercussions that are detrimental and can possibly be alleviated with a measured change over time.
That's how you acclimate fish to the temperature in a new aquarium. That said, it's also how they tell you to boil a frog...
That said, I would assume that short term increased supply would lead to a tighter job market.