Not necessarily.

Back in '96, I had a new hire paired up with me on the job. He had a similar situation as yours, excepting only that the test was a U/A and not hair. He took his U/A, and the day after the U/A, he completed the post-hire paperwork and safety orientation before being put out in the field with me.
Well, exactly 6 working days after his first day out in the field, the General Foreman, armed with a clipboard and assorted papers, appeared in our work area and took the newbee to the side, away from my view. Moments later, the newbee returned to my work area - with the termination slip and his closing check in hand. I later learned through the grapevine that the newbee had tested positive for two different types of (off-topic) substances. The exact reason why it took so long for the newbee to recieve the bad news was never known.