Well, while with the correct connection strings and other variables, I suppose you could run SQL Server 2005 as the only SQL Server and run AC. But, I don't see the advantage.
When SQL Server 2005 installed under default installation, it became the default instance. When AC installed (like most third party programs), it didn't really bother to look for an available SQL Server and simply installed itself as a named instance, in this case "Amazing Charts." You can still configure it with SQL Configuration Manager.
Amazing Charts runs just find under SQL Express and trying to not use it would seem like looking for trouble to me. The Amazing Utilities allows one to detach the databases from the SQL Server, and I am not sure this would work with any other method. Besides, I am not sure that Guardian Angel would support any other configuration.
In the end, though I am no SQL expert, it just seems easiest to install it using SQL Express.