No they don't function as حال or causative adverbs anymore in this translation. Taking it back into Arabic, we realize that the two words that serve as Hal/causative adverbs are no longer. They are now a predicate (the information part in a clause).
Here is a reverse translation of this English version:
Would you take it when this is a slander and (great) sin?
هل تأخذونه حينما يكون هذا بهتاناً وإثماً مبيناً
The two words بهتان and إثم are now predicates of كان (predicates are generally in the nominative case ُ , but with كان the predicate is in the accusative case َ ).
Grammatically speaking, no, they cannot function as Hal/causative adverb anymore in this translation.
Meaningfully speaking, yes, both translations have - roughly - the same meaning, but they are not exact. The slight difference is that, in the original Arabic verse; the words "describe the doer" as having these two characteristics, while in the second Arabic translation; the words "describe the action" bearing these characteristics.
Out-of-topic note: transliteration is how a "single letter" of an alphabet will be translated into another alphabet, e.g. أ for A and ز for Z
We call Quranic translation "interpretations of the meanings", and maybe this is why you can have more than one translation in another language, as long as you keep the grammatical value of the words as accurate as possible.