Nope - It requires that you be paid at least twice per month.

http://www.dir.ca.gov/dlse/faq_paydays.htm

My wife works for a UC school and they post-pay on the 1st of each month. I've skimmed the article you've posted and it would seem that such an arrangement is not allowed.

Do you know how they get away with this, or have any other insight?

Teachers are exempt from this rule.

From here: http://www.dir.ca.gov/dlse/Glossary.asp?Button1=P#profession...

professional exemption

A person employed in a professional capacity means any employee who meets all of the following requirements:

Who is licensed or certified by the State of California and is primarily engaged in the practice of one of the following recognized professions: law, medicine, dentistry, optometry, architecture, engineering, teaching, or accounting, or

Why are those professions exempt?

Honestly I don't know. The objective answer to your question is because that's how exempt professions is defined for the law.

If I had to hazard a guess but I would suspect it's because people in those professions are expected to be salary. Salary is easier to budget out in longer increments as the base pay amounts per pay period typically don't vary. (annual salary / pay periods = pay amount)

Schools are sometimes treated more like a government entity and exempt from certain rules and taxes like FICA, right?

That is my only guess...