You can use any server to host Veeam ONE, but be aware that installation of Veeam ONE components is not supported for the following servers:
- Domain Controllers
- Windows Server 2008 with enabled Hyper-V role
- Windows Server 2008 R2 with enabled Hyper-V role
As to deploying Veeam ONE on vCenter Server, then it is possible, but I wouldn't recommend to do it either.
See this topic for more info: Vcenter 4.1 Crash with Backup V5, Monitor, Reporter
(pretty old thread, but still very useful).