Is it possible to plug a Thunderbolt cinema display into a Mini DisplayPort-equipped Mac and have it work? This question suggests that it's possible and that it's pretty much the same cable, but I don't see any explicit confirmation anywhere.
The short answer is no. Apple's Thunderbolt Display requires a thunderbolt signal (and only that) to operate.
The spec page for the display implies very strongly that Thunderbolt displays will only work with Thunderbolt Macs.
This happens to concern me since I own a previous-generation iMac (pre-Thunderbolt) and really wanted to have the option to use it with a Thunderbolt display. So I asked the guys at the Apple Store.
The Apple Store told me no, it will not work on a non-Thunderbolt Mac.
Sorry to be the bearer of bad news :(.
Plugs are the same, cables are not. The thunderbolt cables contain chips and firmware.
I haven't used the new Thunderbolt display, however I am aware of the following:
MiniDP Macbook -> MiniDP iMac 27: works fine. Thunderbolt Macbook -> MiniDP iMac 27: works fine. MiniDP Macbook -> Thunderbolt iMac 27: does not work Thunberbolt Macbook -> Thunderbolt iMac 27: works fine.
This is in my experience and confirmed from various Apple KB articles. So I believe it's likely you won't be able to use the Thunderbolt display on a MiniDP machine, as that is certainly the case with the iMac 27" models.