Jisho

No, in this word it just means やまい, not はやい.

Here's a monolingual kanji dictionary site.

https://www.kanjipedia.jp/kanji/0002927600

You can see that the primary definition is やまい。わずらい。and that's the meaning used in 疾病.

"Rapid" or はやい is meaning #4, used in words like 疾走 and 疾風.

If you're wondering the, what's the difference between 病気, やまい, 疾病 and so on...

病気 is the most generally used word for illness
やまい has an older feel, being the Japanese-origin word for sickness. It's not used much in modern speech.
疾病 is a more formal word

See this monolingual thesaurus entry for more info on these words and others.

https://dictionary.goo.ne.jp/thsrs/445/meaning/m0u/%E7%96%BE%E7%97%85/

That's a great explanation, thank you so much!! :)