If a chemdraw .cdx file is drag-n-dropped into the Avogadro viewing window, it claims to be trying to read a multi-molecule file (the contents are not this), and then either crashes immediately (OS X) or causes a crash at the next operation (Windows 7).
It reads .cdxml files with no problem however.
I would need a sample file to be able to test further, this would be loaded using Open Babel and so checking it works with obabel would also be useful. At the very least we should avoid crashing.