I think, it's possible but you need to visualization features (Intel-VT-x, AMD-V) on physical CPU for installing ESXi.
If you don't have this features, ESXi will be worked on software mode and all virtual machines which running on that will work slowly.
You can try that and share your experiences.
The only problem is rebooting the Windows Server without logging out of RDC. Am I right in saying 5.5 requires a reboot in order for the machine to load the ISO image for the interactive installer?
There is some ways to unattended installation but I don know that the solution is working on cloud services or not?
For physical server, you can use PXE for installing new ESXi server.
You can see these links:
Thank you!