Yes, 3D Slicer uses vtkThinPlateSplineTransform in its Transforms module to warp images, segmentations, models, markups, etc.
You can try non-linear warping with a convenient user interface by using the “Fiducial registration wizard” module in SlicerIGT extension. You can check out the “U-12 Landmark registration” tutorial on the SlicerIGT training page.
There are many other, more specialized warping modules that rely on this class. For example, Baffle Planer module in SlicerHeart extension is used for warping a thin (or thick) membrane to match an arbitrary-shaped surface specified by a boundary curve and surface points:
