Many legal scholars answer "yes":

[T]he text of the [14th] amendment, the historical events leading to its adoption, the goals of its framers, and the statements of purpose made both by its supporters and by those who ratified it, all point in the exact same direction: The 14th Amendment was designed to nationalize the Bill of Rights and other fundamental rights.

The amendment's origins lie in the anti-slavery politics that gave rise to the Republican Party. After the Civil War, as the former Confederate states began passing Black Codes and other restrictions on the political, economic, and civil rights of African Americans and their white allies, the Radical Republicans of the 39th Congress responded with federal civil rights laws and a constitutional amendment to give them force. ..

 

[T]he phrase privileges and immunities has long been accepted as a legal term of art, employed by no less an authority than William Blackstone in his 1765 Commentaries on the Laws of England, where he defined it as a combination of civil rights and natural rights. Similarly, James Madison and other Founders used the words privileges and rights interchangeably...In any case, the overwhelming historical evidence submitted here is certain to be a major factor when the courts finally get around to restoring the Second Amendment to its rightful place among the Bill of Rights.