I think adding vCloud Director into the mix might overtly complicate things.
vCloud Director would be another layer of configuration to have on top of the existing.
Basically, if you have a vCloud Director installation deployed and ready to go ...
you would restore the VMs into an OVF or vCenter, then import to vCloud Director ... configure them, then power them on.
I know there were some blogs talking about an SRM+vCD overlap, but I'm not sure if that's come to fruition. But this would be specifically for the source environemnt having vCloud deployed there too. However, this wasn't a 'native integration' of VMware Products. it required a fair amount of scripting on top of everything else.
Unless Veeam/Zerto provide the required functionality .... personally, I wouldn't worry about it.