Can I install TFS 2008 in a Dual-tier Configuration Without Admin Rights to the SQL Server Machine?

Yes, you can, but this is not recommended. Although the TFS 2008 documentation requests that the account used to install TFS must be an admin on the data tier, there is a way to circumvent this. The recommended approach is that if, for administrative reasons, it is not acceptable for the TFS Setup account to have administrative rights on the data tier, then to provide temporary server admin rights, and remove these once install is complete. If this route is still unacceptable, then you can do the following:

1. Provide SA rights to the TFS Setup account on the appropriate SQL Server instance. In other words, after the administrator has installed the SQL Server instance on the data tier, the administrator must afterwards give SA rights to the TFSSetup domain account for the SQL Engine.
2. Once the SQL Server instance has installed, add the TFS Setup account as one of the SQL Server Analysis Services administrators. This is needed so the TFS Setup account has the rights to create the warehouse on the data tier.

When you perform the TFS install on the application tier server you will see some warnings, since some of the health checks, via WMI, won't be available due to the lack of server admin rights on the data tier. Thus, there may be lurking issues you won't be able to find. That is why it is recommended that if you don't want the TFS Setup account to have admin rights to the SQL Server machine, you should simply provide admin rights during the install and remove them afterwards. You will rest easier.