It's a slightly inaccurate translation that makes the joke a bit lost. In Russian text, the phrase is "произвести в немцы"; the correct translation would be closer to "to be legally pronounced a German" than "to be promoted a German".

The correct context is given in Chapter IX of Book Nine. The book states that there existed a group of military commanders within the Russian army that were overwhelmingly German and who advocated a gradual retreat into Russia to lure in Napoleon. Ermolov belonged to a different - an overwhelmingly Russian - group of officers close to the general command of an army who advocated a very different approach of not letting the enemy in; in this case, Ermolov's joke effectively states that if Ermolov was German then his opinion would be better heard. Part of the reason for this attitude is that Catherine the Great, who largely promoted the top brass of the Russian army to their current positions at 1812, was German herself, so the influence of Germans in her court was considerable, and was still present in the court of her grandson and preferred successor, Alexander the First.

Note that English translation, at least from the Project Guteberg text, is a bit too straightforward, and spells out exactly the things that Tolstoy only hinted at.