Don't know about Cobras, but I did have to add subframe connectors (welded) in my '96 GT. It did have a strut tower brace and extra lower braces since it was a 'vert. After installing the subframes it was pretty tight.
But, my '05 'vert was significantly tighter than the '96 right out of the box. I did however add a strut tower brace from Strange Development. Hard to tell if it made much difference. I think it did.