Technically it is possible to do in Unity, well to a degree. A basic TB style game could be made with the indie (free) version but it wouldn't have anywhere near the complexity where gameplay is concerned. The main issue being their ragdolls like staying as ragdolls (eg flopping and not moving), and multi-mesh 'characters' can be a nightmare to dissemble and keep that way - you'd literally have to force the objects to stay split and recalculate the physics after everything else (thus having to do the majority in lateupdate).
Gameplay like Sumotori dreams would be incredibly easy to do in Unity, personally I wouldn't attempt to do TB in Unity, too much to calculate inbetween rendering the screen would kill it.