Can TransMagic convert the STL (or any polygonal) format to a CAD format such as IGES, STEP, ACIS, Parasolid, etc?

TransMagic does not convert *.stl (or any other polygonal) format to geometric formats.  The reason is that *.stl files and other polygonal formats are comprised of triangular polygons vs. true geometry such as spheres, planes, torus, cones, free form surfaces (NURBs), etc.  The conversion from true geometry to triangles is very easy (CAD to *.stl); however, the inverse, *.stl to true geometry is very difficult.  In fact, no software actually does this automatically as there is simply not a straight conversion.
There are some reverse engineering software's out there that will take a point cloud (which is essentially what an *.stl file is) and with significant user intervention, they are able to map NURBS surfaces to these points; however, in most cases the user has to define the boundary curves manually.  This process is extremely tedious and difficult as there are many ways to introduce errors into the reverse engineering process.

Further technical information:
TransMagic could very easily take an STL file and generate a geometric file using a technique known as a Polygon Point Mesh Body (PPMBody).  A PPMBody is the conversion of lightweight planar polygons (always found in STL and other visualization formats) to true geometric planar faces in a solid body.  One of the primary drawbacks of a PPMBody conversion is one of file size explosion.  For example, if the STL file had 400,000 polygons - which is typical or even small for some models (such as a medical model) - the resulting geometric solid model would have 400,000 planar (and triangular) faces.  This could be done automatically with no user intervention.  The problem is that the 400,000 polygon STL file that was maybe 3 MB could now be 100 MB in a geometric format.  This is because instead of just a "bag of triangles" like an STL file, you now have solid topology (the glue that holds a solid model together).  For every triangle in the STL file, which originally consisted of 4 pieces of information: 3 vertices and a normal, you'll now have:

1 body
- Under which is:
  - 1 Lump
  - Under which is:
    - 1 Shell
    - Under which is:
    - 1 Face
    - Under which is:
      - 1 surface
      - 1 loop
      - Under which is:
        - 3 edges
        - Under which is:
          - 3 coedges
          - 3 curves
          - 6 vertices
          - 6 geometric points
So one can imagine how a file would grow from 4 pieces of information for each triangular face to 27 (and this leaves some information out!).