Yes absolutely table less design plays major role in SEO. Review any corporate websites example. adobe.com, novell.com etc.. all of they has table less desing.
Why wordpress blogs are most seo friendly.
They are tableless.
Recently we done experiment on table less design.
our site is www.comogroupap.com.au
(note: table less design for inner pages only.)
you can search for "australian seo experts" we are at top 1. and now trying for "seo australia".
For table less and seo friendly tips: http://www.comogroupap.com.au/seo-friendly.php
The live proof i can give you is in google search for "Tableless seo friendly design" or "Tableless seo design" www.comogroupap.com.au/seo-friendly.php
will be in top 2 to 5. Again this is a table less seo frindly desing.