Not according to Cisco.
I did some searching and found a comment from Michael who said this regarding the CVR-X2-SFP with the cat6500 WS-X6708-10GE module:
"10GE hardware ASICs and baseboards were designed long before TwinGig was an option. We cannot support this interface on existing 10GE interfaces because we simply do not have the architecture in place to support GE traces to 10GE ports."
The TwinGig Converter CVR-X2-SFP, shows up as compatible with other platforms, but not the 6500, as shown here:
I hope you can find a solution.