That's what an NC Appeals court ruled when the issue of random drug testing of teachers in Graham, NC was brought before it. I'm not sure about the constitutionality here, but I do have an opinion of random drug tests in general.
Random tests are going to catch two kinds of users: people with serious chronic drug problems, and someone who occasionally uses marijuana. I'm just fine with someone catching the first, as they don't need to be responsible for the care of children while under the influence, and are likely to have difficulty regulating their drug use/abuse enough to not be high at work. However, I'm not ok with penalising someone who smokes a joint in their basement on a Saturday with Pink Floyd playing in the same manner. The issue here is the marijuana a) stays in someone's system a lot longer than more dangerous substances (a couple weeks to a month, from most sources, as compared to a matter of hours or a day.), and b) not nearly as harmful a substance physically/mentally as things that aren't going to be caught (like the teacher who decides that weekends=cocaine). Drug testing someone because they do something stupid or appear to be high at work, now that I'm fine with.
This may be a case of my pro-hippie bias coming through. From my personal experience, and most statistics I've seen, potheads aren't aggressive or harmful to other people, they're simply lazy. Don't get me wrong, I wouldn't want a chronic pot user teaching my kids, if I had any, because I can't picture that being an effective teacher.