If I apply at the Social Services Administration in WA and fail a drug test (marijuana), will I not receive the job?

Marijuana is not "legal" anywhere in the United States. It is still violation of Federal Law, even in Washington.

I think only human resources for that organization would be able to answer that question definitively, but it stands to reason that if you're applying to a federal agency and that agency requires a drug test, you will likely not be hired if you are consuming marijuana since marijuana is illegal under federal law.

This is not something that is determined by criminal law or statute and is instead a question for the employer. If they adopt federal law as far as their requirements for use of drugs, then you may very well be declined the job.