I think it simply checks the DateModified property of the files.
So use SWDocumentMgr to build a list of references, starting with thed drawing and then working your way down the assembly structure.
At each stage, check if the modified date of any of the files is later than that of the parent.
In the example I have attached (OutOfDate.sldprt), eDrawings detects this problem on a single Part that has no external references. This also works for assemblies, even when eDrawings has no access to any of the files contained in the assembly.