Not being too much of a linguist but ever ready to expound on the concept of economy in speech: We have a strong pressure to minimize communication effort both for speakers and for listeners. I would assume that genders help disambiguate and aid the listener discern words with higher certainty without increasing the syllable count.
Our mind builds hypotheses of the words to follow while listening to a sentence. Without this, we couldn't follow a conversation. You can decide faster on what you heard the more the words preceding a noun preclose on the choice of noun. So gender can make communication more robust over a noisy channel, or more compact over a clear channel.
In the midst of a German sentence, some nouns will be precluded because they would be impossible due to gendered articles and adjectives. This lessens the cognitive load (of the trained listener) or conversely allows omitting words when the gender narrows down the selection enough.
I'll go further out on that limb conjecturing that if you haven't been exposed to a gendered language as a kid, that facility will be untrained and quite the bother to acquire as an adult. If acquiring it as an adult is possible at all.
After all that wild guessing, I should close with the observation that in this case German would be more difficult to learn than ungendered languages, _for untrained adults_.
To close off (and to partially answer your question) I'll just say that gender takes little neurons overall in the habit that is language. Whether it'd come out a net plus in syllable economy I can't say.