You wont know until you try. Every home is different, so no one can truthfully answer that question if they don't live there.
Give it a shot, if it does not sound good, you can always move it back.
My recommendation though, would be to bit the bullet and get a Sub Mini for upstairs.
Note that a subwoofer can only be bonded to one Room. You’d likely have the wrong content playing on the subwoofer or be using the wrong Volume control for the subwoofer.
Grab a long extension cord so you can move the Sub around without having to power-cycle it and try everywhere you think might work out.
Also…know that it you use iOS and that device was used to TruePlay your home theater the sound characteristics will be changed….probably for the worse
You could try it and see, or rather hear, but you will get far more pleasing results having a sub for each floor.
Subs work based on being able to pressurise a room and you will be trying to fill two rooms. While in the same room a sub is not usually localised, even at the top of an open stairwell, it will be obvious the sub is upstairs and not in the same room when downstairs.