Is the AutoCAD® 2013 DWG format supported in Enterprise PDM 2012 or older versions?

No.

AutoCAD has changed the DWG format for the 2013 release – see details via this link:
http://usa.autodesk.com/adsk/servlet/ps/dl/item?siteID=123112&id=18801721&linkID=9240617

If you try to add or work with files saved in the DWG 2013 format using Enterprise PDM 2012 or older you will see errors such as:
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SolidWorks Enterprise PDM cannot read or write the contents of the file ‘filename’.
This can happen if the file is corrupt or if it is of a newer version than SolidWorks Enterprise PDM can handle.
Do you want to proceed anyway?
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Could not save data to file.
SolidWorks Enterprise PDM does not recognize the file format. This can happen if the file is corrupt or of a newer kind that Enterprise PDM can handle.
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Enterprise PDM 2012 and older supports up to the DWG 2012 (which is same as DWG 2011 and DWG 2010) format, but not DWG 2013.

DWG 2013 format support is planned for a Enterprise PDM 2013 service pack release (it is not available in 2013 SP0).