I don't know if they do anything with it at all.

Let me tell you a reverse story. Shortly after 9/11 (literally within a few days of it) my son, who was born in raised in Israel and has a heavy Hebrew accent but is an American citizen by birth, arrived in the States.

He wanted to visit friends in Ontario and tried crossing into Canada via the Peace Bridge. He was refused entry. Canadian officials said they did not believe he was going to visit Ontario and accused him of going to work there. (Personally, I suspect that his accent and poor English made them suspicious of the validity of his American passport.)

He called me and asked what to do. I told him to go to the Rainbow Bridge (so as not to run into the same official) and when asked why he was entering Canada to say that he wanted to visit Niagara Falls for a day. He did that, was granted entrance with no problem, and then continued on his way to Ontario.