This could be two people, but would normally be written with a different separator: "Betty, a maid; and a cook" (just removing the comma doesn't help because then Betty could be a maid and a cook). As-is, the implication is that this is three people. If you would like to make that more explicit, you would instead re-structure the sentence†, so it's not highly relevant to the serial-comma-vs-no issue.

†For example:

Betty, one maid, and one cook.

Betty, and a maid and a cook (a little awkward)

A maid, a cook, and Betty (depends on how you want Betty's inclusion to land for the reader)

Right, you can change punctuation to clarify it. However, it doesn't change the fact that the Oxford comma could make the list readable as a parenthetical phrase.

I'm not saying the Oxford comma is bad. I'm just saying that it isn't 100% perfect as many people imply.

Three people; otherwise it should be, "They went to Oregon with a cook, and Betty, a maid."

Or better yet: "They went to Oregon with a cook, and maid named Betty."