Yes, the 15th amendment lead to racial equality, because it prohibits people from making decisions based on race. A person cannot discriminate against another based on race, and if the person does, the person who is discriminated against can sue the person. It is a good way to make sure we treat each other fairly.
I do not believe the fifteenth amendment lead to racial equality, but it was a step in the right direction. The fifteenth amendment addressed some of the issues African Americans had, particularly in the south, where Caucasians were still trying to limit their ability to vote. It did help move equality forward, but it didn't solve the problem.
To say that anything lead to racial equality would imply that we have racial equality. This is not yet the case. If you look at any measurement of outcomes, you will see that the United States does not have racial equality. Two simple and quick metrics are the number of young men in prison (black men comprise 13% of the male population but 39% of the prison population) and Fortune 500 statistics (white men make up 73% of Fortune 500 Boards, while non-white men only make up 10%). We have a long way to go to achieve racial equality (and only then can we start looking for what lead to it).
The 15th Amendment stated that the right of a US citizen to vote "shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude." However until the Voting Rights Act of 1965 became law white controlled local government always found means to deny blacks access to the polls.