Not sure what you mean by "apart from SAT". But if you have musicians playing along with a 3-part choir, the instruments will be playing the root of the chord themselves, so it's totally OK to leave out the root for the choir and have one of the parts sing the 7th instead.
Even with an a cappella song, you could probably still do it, but it might sound a little unusual (in my opinion the listener would probably still "feel" the root in the chord with their mental ear so it would still sound like a 7th chord, but if they didn't fill it in mentally then it would sound like a diminished chord).
And, of course, with a 4-part choir you can give the 7th to one of the parts and you still have a full chord.