No, they are not required.  

After reading the Michigan instructions for filing by mail, there is no mention of needing to include W-2s. 

The information reported on Schedule W takes the place of sending in the W-2s.  In fact, the instructions for Schedule W specifically say not to send the W-2.

To take a look for yourself, here is a link to the instruction booklet.  The instructions for filing by mail start on page 4.  The instructions for Schedule W start on page 40.

https://www.michigan.gov/documents/taxes/MI-1040_Book_642356_7.pdf