It should work, however Id be worried it wouldn't get the full resolution from the Cinema (Depending if its a 20/23/30, which were the DVI based Cinema Displays, and NOT the rare 22" DVI-D one from 1999 (It was acryllic, not silver and generally forgotten). A MiniDisplayPort to DVI straight conversion would be a lot easier, and if its a 30" You'd need MDP -> Dual-Link DVI to get the full res, if its lower, it *should* work okay I think.
HDMI supports 1920x1080. Cinema displays are 1920x1200 resolution, and if you try to input a non-supported resolution they just go black.
Just go MDP to DVI.
EDIT for clarity. HDMI can support 1920x1200, but frequently strips out EDID information and so forth, causing problems with long display chains like this one.