I don't know about that. From what I've been reading, Touches will NEVER come with 2.0 installed. Apparently several people over at Mac Rumors have called Apple numerous times as well as having asked in Apple Stores about whether or not Touches will come pre-installed, and they've been told that they will not. It's considered an optional upgrade. Additionally, most people who have requested getting a waiver on the fee for their Touches purchased after the 11th have been denied by Apple.
My girlfriend purchased a Touch earlier this week at an Apple Store, and it does not come with it pre-installed.
So I highly doubt that your Touch has 2.0, and I would count on having to pay the $9.95 for it. The good news is that it's easily worth the $9.95; although, it's pretty unstable right now. Expect a new update in the near future...I hope.