Probably not, though we don't have a lot of information on translating sentence fragments and how much Klingons do that.
One full sentence reply could be maQongpu' 'e' wImev We have stopped sleeping. In Clipped Klingon, this would probably be Qongpu' 'e' mev. It is the same number of syllables as not anymore, so I'd call that abbreviated enough to match the original.
-taH marks the action as an ongoing one -- it's similar to the -ing ending in English.
For simplicity, we equate the two on this course, so SuQong'a'? will accept translations of "Did you sleep? Do you sleep? Will you sleep?" and SuQongtaH'a'? of "Were you sleeping? Are you sleeping? Will you be sleeping?".
Yes, you can just ask SuQong'a', and most of the time that would be the better sentence. You're really asking whether they're asleep, not whether they're experiencing ONGOING sleep, or whether they're STILL asleep, which is what the version with -taH is asking.
Unfortunately, the course creators have decided to make -taH equal to English progressive tenses, which it's not.