1script - 6:45 pm on Jun 26, 2010 (gmt 0)
This is very relevant for me, so I'd be so happy if you could provide a few more details :)
I can guarantee you from the past week's experience that there is. I have a client whose highest traffic page fell from #1 on two big query terms to pages 3 and 4. What they did was change (not tweak, demolish) ALL the body content and the page template.
First off, I am the first to admit that I am prone to doing what your client did and sometimes even couple times a year ... Every time a nicer WP theme comes along, I am tempted to download and install it on my blog right away. The thinking was (until I read your post that is) that the pages are going to have the same backlinks, URL and structural elements (title, h1,h2 etc.) as well as content, so why should it matter so much?
So, are you at liberty to divulge the difference between the old template and new in your client's case? Say, H1 moved 20 lines down or up, a block of JS moved up or down, content moved up or down, stuff like that. Any additional detail will be greatly appreciated (and probably save me from pulling too much of my hair out the future :)