Simply put…no. A person’s conscience is the faculty that warns you you’re doing something wrong or neglecting to do something you should be doing, but it doesn’t work in a vacuum. Nor is it even innate. Therefore, before one can actually follow their conscience, the conscience must first be formed and told what’s right and wrong. Although Scripture states that our souls thirst or long for God, our conscience starts out as an empty slate and it is up to our intellect to learn the differences between right and wrong. The Church, then, is what helps to keep these differences separated.
In other words, if you were to learn that stealing is not a sin, and if you really believe it, your conscience won’t bother you when you take things that don’t belong to you. If you learn that fornication is not sinful, no warning bells will go off when you engage in it. A person’s conscience must be formed properly.
Although every Christian has a duty to follow their conscience, they have a greater duty to form this conscience along the moral teachings of the Church and by paying strict attention to Holy Scripture. Neglect these, and you will end up with an empty conscience; one which won’t be able to guide you at all.