If you're on the last day of your natural period... No, it may not help at all. Not unless you started the first day of your natural period. It takes 7 days for the hormones in the birth control pills to hypnotize your ovaries. If you are someone who ovulates shortly after your period, then your ovaries may not be hypnotized in time, and could pop out an egg.

If it is vital that you not become pregnant, I would advise Plan B as soon as possible. If you have a plan for an unplanned pregnancy that you are willing and able to go with, then your risk acceptance may be such that it'd be okay to bet on not-ovulating before the hormones cut in.

Either way, you can take a pregnancy test and have good confidence in a negative 19 days after the sex in question.

Good luck!