Short answer: No.
The drug is said to provide access to the 'unused' portion of the brain. This in itself is a misunderstanding of a joke made by Einstein. He said that most people only use 10% of their brain, not as the movie states 20%. However when he said that he was saying that most people never question what goes on around them instead being quite content to just go along with what everyone else is doing. Like little mindless sheep. The truth is that humans already use almost 100% of their brains capacity, with each section of the brain performing different functions from breathing and keeping the heart beating to walking and talking. So a drug that allowed for use of more brain tissue would be almost useless as it is all being used now. However there are classes of drugs that can help to improve the functioning of the brain like stimulants (caffeine and amphetamines are some) that help to, if you like, speed up the brain giving a feeling of clear headed ability. But no drug has been invented that could give the user 'limitless' mental ability, there is no way to do it. If someone where to try they would very quickly encounter issues like information overload and psychological/physical stress.
Lab Tech and ambo