No. Marx advocated for a party and the takeover of the state by socialist/communist parties, but not a vanguard party. The idea of a vanguard party was very much centered around the Bolshevik/Menshevik split, with Lenin and the Bolsheviks advocating for a then-radical idea of a small core of Very Ideologically Correct revolutionaries giving marching orders to the masses; while the Mensheviks advocated for the then-more-traditionally-accepted Marxist position that a socialist movement is not just for the masses, but also by the masses.

The core distinction between Marxist Communism and Anarcho-Communism is essentially that Marx believes you have to take over (or create) a state first in order to suppress the economic conditions that lead to elite concentration of power, and only then can the state be done away with. Anarcho-Communists believe that the intermediate position of taking over the state is unnecessary, that it can be abolished directly in the same stroke as the revolution occurs.

There are often other quibbles too - such as whether economic development is a necessary prerequisite for a modern stateless society.