I work for a union as well, and I believe the practices vary from company to company. It all depends on what the contract terms are between the union and the company. At my work we are required to take a pre-employment drug screen and we are required to take a drug test if we suffer an injury that requires medical attention or if we do more than 1000$ in property damage. Other than that, I never get screened.
One thing you can be sure of though is that there will be a probation period where you are subject to a drug test at ANY TIME. It'd be a good idea to abstain for awhile until you get past the probation and get a clear understanding of what their drug policy is.
Good Luck.