Translation:The man whose wife is a police officer is here now.
I think that's taking it a bit too far. We already accept a police, which is considered incorrect by many native speakers, and not accepted in most other Duo courses as far as I know, but skipping the article too would be even more non-standard.
(If anyone wonders about 'a police', see here: http://www.grammarphobia.com/blog/2014/09/a-police.html)
The answer that showed up on my screen was: "The man whose wife is a police is here now." In English, this does not actually make any sense.
In English, you could say, "The man whose wife is police is here now," but that would be very unusual, and would sound "clunky" to most native-English speakers. Also, DuoLingo did not accept that version. Most often, we would say "a police officer," "a policewoman," or "with the police."
In direct answer to your question, yes, the word "officer" would need to be stated in order for the statement to read or sound correct in English .