Maybe it's just that the constraints are the same color as the background, but even when I went deliberately trying to see them by moving the hip up that the feet lift well off the floor, I don't.

Anyway, the alternatives to using IK are either manually adjusting the positions of the arms/legs to keep the hands/feet in the correct place, which is tedious and not super precise, or you could try Richard60's suggestion of using Constraints. I have not played with that myself.

But IK generally will do what you want. I would just suggest saving before you turn it on/off, and then check things are ok. Set keyframes to avoid them getting messed up by the switch. The whole thing about targets is largely moot if you aren't moving the body so far that the hands/feet are getting dragged away from their starting point.