This issue would appear to have been noted now, at long last, by the developers. I just upgraded to the latest (2.0.7) version of the WC plugin and noticed the following error message had appeared:
"In order for database caching to work with WooCommerce you must add _wc_session_ to the "Ignored Query Strings" option in W3 Total Cache settings here".
See screenshot here:
http://matchlessclueless.com/wp-content/uploads/2013/04/Capture.png
This is interesting as I had previously added "wc_session_" (i.e. no underscore at the start) to the list of ignored query strings and this seemed to have worked for me, so not sure of the difference or significance between the two versions of "_wc_session_" and "wc_session". I have both added now just to be sure anyway.
James