No, they generally just walk across our Northern border.
The first illegal immigrant (at least the first one who actually admitted it to us) that my wife and I met when we moved to California nearly 33 years ago was a French Canadian who had been living here for about 5 years working at his father-in-law's bakery. They were from Germany and while they were 'legal' they had not yet been naturalized. Eventually Pierre got caught, but it only took one trip back to Montreal and a couple of letters from his wife's parents and he was back in SoCal with a valid working visa. But then he was 'white' and didn't speak Spanish.
And the first illegal Mexican I ever knew was when I was still working back in Michigan in the 70's. He was one of the draftsmen in our office. He grew up assuming that he had been born in Texas but raised in Michigan. He had gone to school, graduated from high school, went to community college and finally got a job at our company. He eventually met a gal and was planning to get married and while he had no birth certificate (both his parents were killed in an accident when he was still in school and so he lived with relatives who had told him that he had been born at home and that they never knew if he even had a formal birth certificate) he did contact his parent's old church back in Texas for his baptismal records which he needed to get married in the church in Michigan (he and his fiancé were Catholic) and it was only then that he discovered that he had actually been born in Mexico and was technically 'illegal'. He finally got things straightened-out but it took about a year, all the while his wedding was on hold, but in the end a lot of people went to bat for him, our company included, and so it all ended well.
These are just two stories that I can personally relate, and in both cases, they do not fit the stereotype of what people are constantly claiming is happening, that ALL illegals are 'brown' people jumping fence from Mexico or that they're living here under the radar, collecting welfare and not contributing to society.

OCU