No, the OCC algorithm doesn't directly allow this. The thickness algorithm expects a solid as input and a list of faces which will be removed. However, it's possible to give only a face or a shell as input or an empty list of faces to be removed but then the result is the same as you get with the offset.
So, if I got you right then you want to create a solid out of the input shape, the offset shape and filling the sides. On the offset function there is a fill option which should do exactly this but until now it works for simple cases only. The biggest problem is to fill the sides. The thickness algorithm must do the same somewhere but I didn't find the relevant code section.
The edges are extruded normal to the surfaces.
The offset does it the extrusion as you need it? The actual extrusion algorithm in OCC works differently. There you can define only a single direction for the whole face.