Is "贪得无厌" the best choice for this sentence? This is the original text:

Drifters of this world are the collectors of forgotten knowledge, lost
technologies and broken histories. Our Drifter is haunted by an
insatiable illness, traveling further into the lands of Buried Time,
hoping to discover a way to quiet the vicious disease.

This is my translation, and I am unsure about the second sentence:

这个世界的流浪者寻找被遗忘的知能，丢失的科技，和破坏的历史。被贪得无厌的疾病困扰的流浪者不得不深入埋葬时间之地，但愿能从这个残忍的疾病找到平安。

I looked up &quot;insatiable&quot; on google translate and it gave me &quot;永不满足&quot;, which I think means &quot;impossible to satisfy&quot; but I'm not sure if it fits. Based on my knowledge it sounds like something specific to eating food.
After digging around for some synonyms, I stumbled upon &quot;贪得无厌&quot; which google translate also says means &quot;insatiable&quot;, which seems closer to &quot;relentless greed&quot;, but I'm also not sure if this is the best choice.
贪得无厌 -and/or- 贪得无餍 can be found in almost any dictionary.
ABC defines it as:

be insatiably greedy

Oxford defines it as:

have an insatiable greed

So we can kind of see where Google Translate's insatiable came from.
MDBG has a rather unique translation too that you can consider:

avaricious and insatiable (idiom); greedy and never satisfied

Wiktionary

(idiomatic) greedy, avaricious

I'm not sure where your Chinese excerpt came from but it's not written particularly well to begin with.