That's a myth, the origin of the colors are not known for definite, there's a few theory’s around it.
There's no separate tag or flag for a greater Germany, although now that you mention it, it could be interesting to mod it in. I wonder what flag it would have. Would Swiss or Czech be accepted cultures?
Let's argue about this.
From wiki:
"The German association with the colours black, red, and gold surfaced in the radical 1840s, when the black-red-gold flag was used to symbolize the movement against the Conservative European Order that was established after Napoleon's defeat.
The Frankfurt Parliament had declared the black-red-gold as the official colours of the German Confederation, with the red in the tricolour most likely referencing the Hanseatic League, and the gold and black symbolizing Austria as its empire, considered to be "German", had an influence over (what would become) southern Germany. There are many theories in circulation regarding the origins of the colour scheme utilized in the 1848 flag. It has been proposed that the colours were those of the Jena Student's League, one of the radically minded Burschenschaften banned by Metternich in the Carlsbad Decrees. Another claim goes back to the uniforms (mainly black with red facings and gold buttons) of the Lützow Free Corps, comprising mostly university students and formed during the struggle against the occupying forces of Napoleon. It is during the mid-nineteenth century that red became synonymous with revolution and Karl Marx's socialist vision. Whatever the true explanation, these colours soon came to be regarded as the national colours of Germany during this brief period, and especially after their reintroduction during the Weimar period, they have become synonymous with liberalism in general."