Thank you for your patience.
GroupDocs.Annotation for .NET API use the "StoragePath" as base path, all required files and folders like temp also created at "StoragePath", so it is possible to utilize any required path.
In LB scenario each hosted instance will also use the "StoragePath" so if it is shared path between different hosting then it will be utilized.
Currently in open source front-end MVC/WebForms applications we have used the application "App_Data" folder like you can see here
and which can be changed as per your requirements.
Please make sure to change all "App_Data" folder hard-coded path in our existing open source front-end MVC/WebForms, if you change to other folder location.
If you will need any help or you will have any other questions regarding GroupDocs.Annotation for .NET API please feel free to ask.