No, that is not what this case is about.  The case does deal with state powers and federal powers, but it does not use the 14th Amendment to apply the Constitution to the states.  That idea, known as incorporation, did not come about for almost a century after the McCulloch decision.  (For one thing, the 14th Amendment did not even exist at the time of this case.)  The McCulloch case was, instead, decided on the basis of the “necessary and proper” clause (also known as the “elastic clause” of the Constitution and on the general idea of the supremacy of the federal government.

The major issue in this case was whether the federal government had the power to create the Bank of the United States.  There is no clause in the Constitution that explicitly gives Congress this power.  However, the Supreme Court held that the elastic clause gives Congress the power to do anything that is “necessary and proper” to the carrying out of the powers that it is given.  The Court held that this power included the power to create the bank.  This had nothing to do with whether the Constitution applies to the states.

The case did say that states cannot tax things that the federal government does.  However, this was not decided on the basis of the 14th Amendment.  Instead, it was decided this way because the power to tax federal activities would give the states the power to essentially overrule the federal government.  Since the federal government is supposed to be more powerful, this could not be allowed.

Much later, the 14th Amendment came to be used to apply the Bill of Rights to the states.  However, this could not have happened at the time of McCulloch v. Maryland.