Georgia HB 87 (2011) and its unintended consequences say otherwise. While the H-2A is indeed popular, there are still a staggering number of people working these jobs who are here illegally.

https://www.forbes.com/sites/realspin/2012/05/17/the-law-of-...

https://www.npr.org/sections/thetwo-way/2011/05/27/136718112...

https://www.theatlantic.com/business/archive/2011/06/georgia...

https://www.politico.com/story/2011/06/ga-immigrant-crackdow...

https://www.timesfreepress.com/news/2013/jul/07/immigration-...

There are a massive amount of overstays on H2A & H4 visas. They didn’t arrive here illegally, but their current status is very often illegal as they can’t switch jobs or extend beyond a season without a cumbersome renewal process, often which requires leaving the country for at least 3 months.