Well a lot of what has been said here is true and false so I'll throw in what I was taught about it.
(I'm studying Psychology so I had to take a lot of courses on this in case you were wondering why you should believe me)
Without knowledge of what the substance is, you won't become addicted to it specifically. Depending on the person, you *could* become addicted to the effects of the drugs after the first use. It really depends on the person though. For some people, it does take prolonged use of a "hard" drug to become addicted but people who have a family history of addiction or simply are so low in their emotions that the high is the most amazing thing in the world, they CAN become addicted after the initial intake. In your scenario however, the person wouldn't know what caused the high. More than likely, they would drink whatever they were drinking (that someone slipped the drug into) that caused the high.
That being said, some people really can just get high once and never do it again. Psychologically, people who are experiencing depression or some sort of mood altering disorder will become addicted much faster than normal. The risky part in your case is that the person would have no idea how they got high. If they *did* become addicted after the first go, they would obsess about it until they got whatever it is that caused them to become high.
You have to keep in mind there is Psychological and Physical forms of addiction. Physically, it's not likely you would become addicted. Your body would not create a dependence on it *that* quickly normally and the chemicals wouldn't be thrown out of whack that quick. Psychologically it is very possible. But as with everything, there are exceptions.
To answer your question in the most summarized way I can think of:
Yes, it is possible to become addicted to the substance after that first taste. If the person did not know what the drug was, they would attempt to find whatever it was that caused the high. They would probably start with the drink and keep going further and further until they knew how to get the high. You CAN become addicted after the very first encounter with it but it's mostly a psychological addiction. Genetically, if you have a family history of addiction, you could become Physically addicted on the first encounter as well. It depends on the person but I believe the average person would NOT form the addiction. It IS possible, but unlikely.