In answer to the question in the title of your post, yes, you are supposed to answer questions about illegal drug use truthfully. Applicants for positions of public trust have an ethical obligation to answer relevant questions honestly. While your past drug use would presently preclude you from employment with, for example, the FBI (see current employment drug policy), it would not necessarily preclude you from holding a security clearance with another federal agency.

Keep in mind, however, that telling the truth is no guarantee that you will pass a polygraph examination, as many have learned the hard way. The "test" depends on trickery, not science, and while you may (and should) be completely honest with your polygrapher regarding relevant issues, your polygrapher will not be completely candid with you, as polygraph procedure depends on the polygrapher lying to and otherwise deceiving the person being "tested" about the nature of the procedure. Worse still, the "test" is inherently biased against the most truthful examinees. You'll find these deceptions exposed in Chapter 3 of The Lie Behind the Lie Detector. Chapter 4 provides suggestions for reducing the risk of a false positive outcome.

Lienot,

The option I suggest to Jinsankon -- and to all -- is to answer relevant questions honestly and to make an informed choice regarding whether to use countermeasures to protect against the risk of a false positive outcome.

Yeah, I am very uncomfortable taking a polygraph test. I feel that it is a gross violation privacy, and if I cannot be trusted at my word, why should I trust them at theirs? Not to mention that everything I have read states there is no scientific evidence to support that the contraption works. Something about trusting my fate to someone that can ruin said fate by simply not liking me, is an absolutely horrible thought. 

Sadly, if I don't do this I cannot work for this specific organization. It makes me feel kind of dirty to actually choose the side of evil just to get a job(like I am selling my soul to the devil)...

I will be completely honest with the polygrapher, and if I fail or if I don't obtain a clearance based on drug use from many years ago, than oh well.

(By the way, I saw the segment you did on British TV with the gentleman from Shaun of the Dead. Kudos for that, it was informative and entertaining)

Sarg, 

I agree that you are doing nothing unethical, you are telling the truth.  Nothing more is asked of you, and mental math is a great idea.

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Did they put in writing that your selection was random? If so, please post the exact language. 

Another thing you might do is ask for details about how you were randomly selected, in a Privacy Act and/or FOIA request. A Privacy Act request is where you could ask how you in particular were selected, and for your records. A FOIA request would be a way to ask how the random selection in general is being performed, when, and by whom.