We were looking at these units and did many trials with Roland DG, they were very helpful.
The VersaLEC UV LED units will "just about print on anything". OK, not anything, however they are very flexible. When we did trials I am sure that we put similar weight thick card into them.
As for the solvent units...I believe that they have the same capabilities for handling thick media as the UV units - however, the media has to be compatible with the solvent inks. This is critical and a major caveat. Media can be treated/coated to make it work with the solvent printers.
EDIT: The VersaCAMM brochure states:
Maximum 1.0 mm (39 mil) with liner for printing
Maximum 0.4 mm (16 mil) with liner and 0.22mm (9mil) without liner for cutting
Stephen Marsh