Can Alfresco be configured to have the actual application itself running on a different server than where the document repository is located? Our hope is that we can host our repository on an already existing file server and then connect to it across a local network from an application server running an instance of Alfresco. Is this possible?
Sort of. There are a couple of options. But first and foremost they will all require you to import your documents into the Alfresco repository.
First Option. Alfresco pointing to a remote content store. This is the basic starting point of the options discussed here and below. Alfresco can be configured to point at a remote content store through the custom-repository.properties file. This is a remote filesystem mounted on the server where Alfresco is installed. This can be Direct Attached Storage (SCSI, Fibre) or remote storage (think iSCSI, NFS, CIFS, etc.)
Second Option. Alfresco Share. Share can be installed on any remote server and connect over the wire to a central Alfresco repository. It requires, further configuration, but it is just pointing the share application back at the repository. In fact this is part of the point of the Surf framework/Web Scripts and leads to the next option.
Third Option. Custom Applications. With the interfaces available from the Alfresco repository there is more than one way to skin this cat. From the Java APIs, Web Services (SOAP), CIFS, webDAV, NFS, FTP, SMTP, Web Scripts(HTTP/Rest API) and using Surf, you can build custom applications that can remotely connect to Alfresco, allowing you to retrieve, insert, delete or update content from any location. Check out FlexSpaces in the Alfresco forums as an example of this (http://forge.alfresco.com/projects/flexspaces/).