Hello,
To mount this infrastructure you want, is not possible. I have enough EXPERIENCE large infrastructure with multiple VC, with large number of VMs as Host Esxi and do not recommend this design that have you thought.
Note:
Linked vCenter Servers are the maximum 10 (for the link between all the VCs, domains must have trust relationships, if 1dominio per VC)
In linked mode of many VCs you lose Performance.
With the SSO is the same, requires trust relationships between domains.
Design that I recommend:
1 - All Independent site, each with its SSO, VC and SQL.
2 - Install 6 +1 and 6 +1
Obvious that the amount of host must be taken into account, the number of VMs, domains, domains'll have few, if they will have trust relationships or not, etc..
Please look to this article for more information about sso:
vCenter Single Sign-On Part 1: what is vCenter Single Sign-On? | VMware vSphere Blog - VMware Blogs
And look at you this article to see several types of SSO infrastructure design: