Freewheel or Cassette
If the spacing is the same, it should work, although I wouldn't be surprised if the shifting required adjustment every time you swapped, even if the spacing is nominally the same.

The other problem is that a 9-speed freewheel/hub is an inherently bad design, since more of the axle is unsupported, and more likely to bend or break.

It's also possible that the set you found really does have a cassette and freehub, and was simply mislabelled. None of the majors ever made a 9-speed freewheel, or a thread-on hub for a 9-speed freewheel.