The installation grants all of the rights necessary for that service account to run SQL Server.

That does not mean that service account has full administrator access to the server, or - in fact - access to all of the folders in the system.

As of 2008 on Windows Server 2008, it gets even tighter and your service account doesn't even have access to SQL Server. The service is run under the service account - and a special service SID is created - and that service SID is granted access.

So - yes, if your service account needs to do anything else then you need to grant the additional privileges.