I believe that might be the case. Kanji is there for a reason, and using hiragana instead of it for words that are typically written in kanji may create ambiguity. You should do your best to learn and practise all the kanji that you are exposed to in HSC Japanese. You may also wish to consider having a look at sample responses at the band 6 level. As you do, you can try to look for any instances of words that are typically written in kanji being written in hiragana. That can help you better understand the expectations in terms of writing quality.
Using furigana may help if there is a particular kanji that you suspect you may have not written correctly. It can help you indicate the intended kanji, thereby ensuring that you are still conveying the intended meaning of the word/sentence, although I am not certain if it is permitted in HSC Japanese. This is something that you would know more about.
I hope this helps!