Yes, the constitution is still relevant enough to stand as it is currently written, because it has not changed. People just have decided that they no longer like the freedoms that the constitution stands for. As Justice Scalia said, "The constitution is dead! Dead! Dead! Dead!" By that he meant that people should not project their own fly by the night opinions on the constitution.
The Constitution of the United States of America is plenty relevant in contemporary times as the document was meant to be flexible. The Founding Fathers realized that the legal framework had to be adaptable to modern times. The writers of the Constitution didn't know about things like abortion, automobiles, construction codes and drug laws. As such, the 10th Amendment was a key to the entire process as it gave states the right to determine their own destiny with powers not specifically enumerated to the federal government. Our founding document is replete with statements that can be interpreted by legislation and judicial process.
Some parts of the constitution are completely out of touch with today's world, such as the right to bare arms, but most of it holds up. The problem isn't the constitution itself, it's people's interpretation of it. Much like a religious text, it's cited at length when it validates what somebody wants, and dismissed as an ancient document when it doesn't. Overall, it provides a framework that is still useful.
Yes, the constitution is still relevant enough to stand as it is currently written, because it is a timeless document. The ideals in the constitution have to do with human rights, and basic ways to run a government. These ideals do not change, even if opinions change with the times. People who do not like the constitution simply want to do whatever they want, rather than uphold freedoms for others.
The constitution is the one thing that protects people from being used by the government. It does not matter how long ago it was written, it was made to protect the citizens of the country and keep them from getting used and abused by the higher powers in the country.