I don't see why it wouldn't if it is a car with an automatic to begin with. The 700r4(is that what is in there?) that is in there is longer and the mounting place is shorter so these issues will have to be addressed. Getting the converter to lock up might be an issue.
I think there's a guy up north (maybe canada) that has a stage II in a c4 corvette with 2004r.. I could be wrong about the trans though.. but pretty sure that's right.
TCC lockup shouldn't be a problem if the Vette has a 700R4, same wiring would work. The 2004R's rear mount is 5" farther back so C-member would need to be modified. BTO has C-members for 68-79 & 80-81 may have others.
Take a look on Corvette C6 - C1 Reviews, Performance, Parts For Sale - CorvetteForum.com I'm sure someone there would know what parts are available.