Yes, they drug test.
Don't even think of applying if you've recently done drugs, plan on doing drugs, or have ANY type of criminal record, even back to pre-adult - unless it was expunged.
My roomate works for them. Very strict, very.
My old roomate went to apply. When he was 16 he stole a fishing lure from wal-mart - in addition to being banned from walmart for life, he was also unable to get a job at UPS.
Good benefits, awsome union if you do get a job there. almost impossible to get fired, short of stealing something or failing a drug test.