True. It wasn't until the late 1800s that anyone even bothered to track movement back and forth. And until later, no one was kept from coming in, and living here. Took a while to become a citizen, but there were no illegal immigrants, because there was no such thing back in the day.
In a manner of speaking, yes. There were no illegal immigrants in that they would routinely come across the border seasonally and return home unmolested. It is only in the last decade or so that the border patrol has begun to crack down on the ranchers that employed them. This is no doubt a result of the more recent influx of those with less honorable intentions than pursuing work.