Yes, it is possible that going to the main page with cookies disabled will dump your cart contents, since in "some" cases, there is no zenid applied to the "home" link.

Simple solution: don't do that.
More complicated solution: Change all the "home" links to be generated via zen_href_link() instead of the prettier-displayed links produced by HTTP_SERVER+DIR_WS_CATALOG. This way you can satisfy the 2% of users who are too scared to have cookies enabled in their browser even though they're not too scared to share their credit card online while shopping.