Is there an API with Citrix that will allow programmatic access (read) to files on a remote server only accessible via Citrix?
I don't exactly unterstand your question. You should explain what you are trying to achieve.
Are you outside or inside your network? How do you want to access the file? With the use of the ICA-protocol?
You can actually publish files just like an application in Xenapp. But I assume you don't want that.
You should download the sdk from here: http://community.citrix.com/p/sdkcentral#xenapp And also check the corresponding community.