Nnot exactly. Katakana is used for loanwords, and since japanese has distanced itself from chinese language and its readings, the on’yomi readings are de facto loanwords. There’s a reason why they do separate loanwords from the language… english for instance is a complete mess because it doesn’t. Try pronouncing rendezvouz as an english reading for instance…
Furthermore katakana means that it’s phonetic, it means that familiar words that would be in hiragana may appear within the reading, but aren’t actually there.
That being said, you are correct about not hearing the difference in spoken language.
Vocab reading and kunyomi reading are not synonymous though.
本 for instance, is ほん (onyomi) or もと (kunyomi), but it depends on context.
本を読む is ほんをよむ
本を正す is もとをただす
天 usually means “heavens” no matter how it’s read, but whether you read it as てん (onyomi) or あま (kunyomi) depends on where it appears.
In certain terms like, 天の川 (あまのがわ Milky Way) you can’t use てん, but in the phrase 天を仰ぐ (てんをあおぐ look up to the heavens), it would be weird to say あまをあおぐ.