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Don't know for sure, but I doubt the headers would fit.
The C5 Z06 uses a generation III LS6 engine. The LS6 was a redesigned 5.7ltr LS1 engine that had redesigned exhaust manifold along with other modifications. These manifolds are constructed of cast-iron material and have been designed to reduce weight by utilizing thin walls.
The base C6 uses a generation IV LS2 engine for the 2005 - 2007 or LS3 engine starting in 2008. The LS2 is a 6.0 ltr engine and the LS3 is a 6.2 ltr engine. Even though the LS2 uses the same "243" heads as the LS6, that is really the only similarity between the two that I know of.