Well yes, but actually no.

The reason grammatic gender is called gender is because almost all nouns referring to men (boy, men, father, uncle...) are in one group and almost all nouns referring to women are in the other.

In German, Mädchen is not in the female group because -chen is a diminutive changing any noun's group to neuter. The word Jungchen, from "Junge" meaning "(young) boy" exists as well and is also neuter.

Similarily, all plural nouns are in the female group. Just because grammar has some more quirks doesn't mean grammatical gender doesn't line up with actual gender.

The only exception in German I know of would be the word "Weib", cognate to wife, translating to women, which is in the neuter group. Except this word is archaic and an insult nowadays. All other words referring to gendered people should be in their corresponding grammatical group.

Funniest example I know is how vagina is masculine in French.

Linguistically, the term "grammatical gender" is really a historical mistake based on linguistics the discipline being born in Indo-European languages, (twice -- first with the first Sanskrit grammar, then for serious with people noticing suspiciously many similarities between Sanskrit and Latin)

The new and more inclusive term is "noun classes", e.g. Swahili has nine, e.g. "mtu" is person, class "animate/human singular", then you have "utu", "humanity", from the same root but in the class for abstractions. All Indo-European languages have three, and in that context "female gender" is really "the noun class that the word 'woman' is part of", same for "man" and "thing". Girl is neuter in German because it's a diminutive and all diminutives are neuter, "person" is female and "human" male because that's how the language assigned them semi-randomly to classes (mostly through phonetics). Nouns constructed with infinitive+er (like baker, very similar formation rules as in English) are all male, feminists really don't like that because that covers basically all professions... but it also makes all murderers male. Which doesn't make all murderers male, same as me being a person doesn't make me female. Grammatical /= personal gender.

This is all that you can point to a chair (male) and table (female) and have a good chance to be able to refer to them very efficiently, like "his leg is broken" and it being clear that you don't mean the table: That wouldn't make any sense as it's female and you'd say "her leg is broken".

But that’s because all diminutives are neuter in German. Like das Mädchen is the diminutive of die Mäd (the girl) same with das Fraulein (the young woman) is the diminutive of die Frau (the woman). Mäd and Frau are feminine words

It’s also the same in Dutch. De meid (the girl) is gendered (Dutch doesn’t have a distinct article for masculine and feminine words anymore) and the diminutive het meisje (the little girl) is neuter.

At which point you're free to use the feminine gender, because the word for "person" is a feminine noun.