Can Creo Illustrate open native Creo Parametric files such as assmblies, parts and drawings?

From "Help Center" - "Supported Import File Formats for Creo Illustrate": https://support.ptc.com/help/creo/illustrate/r10.1/en/index.html#page/creo_illustrate/visualization/shared/Supported_File_Types.html# 

Hello @wfalco, 

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Thanks,
Vivek N.
Community Moderation Team.

@wfalco You cannot directly open a Creo Parametric model in Creo Illustrate. Instead you need to use the Import so it will create a .c3di file from the Creo Parametric model. 
If you use Windchill then I would highly recommend using Import, Link.