It's the company's discretion on how to handle violation of their policies. One would hope that they would follow what their policies specify and also be consistent with past practice (what they've done in past situations). My personal experience in HR in dealing with this type of situation is that reporting to work under the influence of drugs and/or alcohol is a terminable offense, and working while intoxicated -- particularly if you work with machinery or drive a vehicle -- potentially endangers the health and safety of the employee, coworkers, and others. A simple drug test reveals the truth no matter what the employee says.
I have personally known of situations where employees of other companies have not been fired, however, and have entered into "last chance" agreements with their employers. That was an example of someone who aggressively worked the system with the help of their union, but even they found that their chances ran out eventually. (Meth didn't belong in the workplace, and they couldn't quit.)