Something I’ve been wondering about was if other people could still understand if you accidentally mixed up On’yomi and Kun’yomi reading in jukugo words. If you pronounced 下町 as「かちょう」 instead of「したまち」in a sentence, at a speed of about 2-4 words a second, it’s not going to throw off other people too badly, right?
I guess realistically the listener would ask to repeat the sentence and correct you, but I’m still curious.
No, they wouldn’t be able to understand you in this case or a vast majority of other cases. Depending on your pitch they might think you’re trying to say 課長 at best. It’s no different than how if you said a word with a completely different pronunciation in English people wouldn’t understand.
Indeed, “Shitamachi” is term that describes areas of Tokyo like Yanaka and Nezu. “Kachou” is… not. You’re gonna get some blank looks if you say “I’m going to visit Yanaka to see the kachou”.
I think if I say I am going to visit the Netherlands in New York, you wouldn’t understand me either.
I meant “downtown” but I read down as nether and town as land.
Think of kanji as being no different than english letters (except there’s way more of them). If I told you, “I broke the kip her” would you know what I was talking about? Kip her? What’s a kip her? Turns out I meant “cipher”, see ‘c’ can be read as ‘k’ or ‘s’ and ‘ph’ can be read as ‘f’ or ‘p h’ so it shouldn’t matter right? But the word comes before the spelling.
下 is sometimes read as か and sometimes read as した, but the word is したまち and it’s spelled 下町.
Mind you, there are some words which can take either reading, and even some words for which the reading is fairly fluid, by public consensus. For example, the word 私立, しりつ, can also be read as わたくしりつ, because otherwise it’s a perfect homophone for its antonym, 市立.
大人 is read as おとな most of the time, but when it’s grouped with 中人 and 小人 on a list of ticket prices (for example, this page on the Tokyo Disney Resort website, about halfway down the page), the reading is だいにん instead. (You should still use おとな in general conversation, though - I’m just providing this example so you don’t get too complacent. 
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