Yes and No. You can modify the MIME type by creating a .htaccess file or adding it in the Control Panel to allow for server parsed .html files. Otherwise you will be beter off placing SSI in .shtml files.

You can get away with using .html instead of .shtml if:

In the .htaccess file put:

AddType text/x-server-parsed-html .html

This will allow for .html server-parsed files.