The working profile that you set up in the color settings, determines how Illustrator works with color and displays it while you are working with the file. The profile you embed when exporting should match what the print company tells you. The 2 profiles do not need to be the same, but it helps you if they are.
Usually you will not convert CMYK numbers when saving a PDF (even when exporting to a different color profile). But nevertheless after exporting the PDF, open it in Acrobat and check it.