No. And here's why, but before I tell you that please note I have over 20 years and over 10K flight hours of aviation experience in the Navy as a flight engineer on the P3 Orion. I know how aviation rules of the air work. The sole purpose of the transponder is to allow the air traffic controllers to know exactly where your plane is at all times while in the air traffic control airspace the controller is responsible for monitoring. It the transponder is off you would get radio communications from ATC once they see on radar you are in their airspace. If the pilot doe not respond within a few minutes on the radio to ATC and still doesn't turn on the transponder that is when ATC contacts the military and the military will launch an intercept plane to investigate and try to communicate with the rogue plane. If that doesn't work there's a chance the plane could get shot down if it exhibits hostile intent. Not having your transponder on is a BIG deal in aviation. I don't see them doing that just to hide the fact that they are hauling around illegal aliens. It would actually draw more attention to that airplane than if they just left the transponder on the whole time. Remember, they don't want to stand out and be noticed while doing these crimes, so in this scenario you describe it would actually be counter productive to their illegal mission to turn off the transponders and try to "hide". It would actually highlight the fact that plane is not doing normal flight rules and make it standout even more in my 22 years long aviator's experienced opinion.

If anyone would know it would be MonkeyWerx

It's possible, I suppose. Answering for updates.