Both sentences convey the same idea, but they could be phrased more naturally. Here are more natural ways to express the same information: Can a police officer go on paid leave if they sustain a serious on-duty injury that requires an extended recovery period? Is it feasible for a police officer to receive paid time off until they fully recover from a serious on-duty injury that necessitates significant medical treatment?

until they are fully recovered

Both sentences are very wordy. Both are very good and use the structures that are taught in a/the classroom. second sentences requires "until fully recoverED" "PAID TIME OFF" <- although it works grammatically it sounds unnatural and strained. In the UK British English we use the phrase "sick pay" On the street in daily speak we would probably say Can a police Officer ... (1) and Is it possible .....(2)

#1) It is not clear to me to what period "while performing his duties" refers. You have already said "sustained on duty", so is this just repetition? #2) "fully recovered" The sentence contains more clauses than are needed: "Is it possible for a police officer to receive paid time off while undergoing significant medical treatment for a serious injury sustained on duty?"