I am running Captivate 4 on a Windows 7 64-bit operating system, and this does not seem to be a good idea; although most of the functionality works fine, I am having problems editing items in the library. E.g. when I try to edit a background with Paint or another graphics application, it opens the background, but when I save my changes, Captivate hangs. It does this consistently, and it has been confirmed as an issue by other users (see http://forums.adobe.com/message/2887534). Other users are even reporting issues with capturing 64 bit applications.
So for now, if you want to use full functionality of Captivate and you have a choice between Windows 7 32 or 64 bit, I would go for 32 bit. Lets hope that everything will be fixed in Captivate 5 or with the next update.