Arbitrary means that the action picks one of the pre existing instances setup in the editor and uses it's properties to create the new instance, and you don't get to pick which one. So no it is not a replica.
In that case, if the runtime so happens to pick an instance that was setup to be a template, then it will seem that the action created an instance based on it, but in reality it happened by chance.
In the example if you use an empty string or a string that doesn't match to any template, the runtime still needs to use one of the existing instances as a source, and it is picking the one defined as a template, because it also happens to be the first in the layout. That is not a behaviour you should rely upon as it is an implementation detail of Construct and could change at any point.
The only way to guarantee which instance is used as a template when creating new instances is to provide a name of an existing template.