There is absolutely correlation between sessions. If visitor 1 (corresponding to sessions 1,2,3) has a high conversion probability, while visitor 2 (corresponding to sessions 4,5,6) has a low conversion probability, then you've introduced correlation between sessions 1,2,3 and sessions 4,5,6. This breaks the CLT and all the usual independence assumptions.

If most of your visitors only have one session this may not matter...but then again with only session cookies you don't even have a way to know this.