Local texture references will not work on the farm as you have already found. This is similar to problems in building websites where locally referenced images work perfectly fine as long as you only browse from that computer.
For most large scale pipelines, artists do work in a centralized network storage space and normally use production pre specified paths for location of assets such as textures and geometry.
In terms of using local data one could potentially use the maya dirmap features to remap local drives such as C: to a network path such as \\mycomputer\C$ The only catch is that you're basically limited to 10 connections as well as opening up access to all the data on your host to other hosts. Vulnerable directories such as C:\WINNT or C:\WINDOWS are probably best left unaccessable, even in the most secure facilities.
A simpler alternative if you are using auto-mounting is to map a portion of your c:\ drive to another drive letter and to only work in that drive. The auto-mounting will remap the drive correctly on the worker automatically. Again you are limited to just 10 simultaneous connections so this isn't a scalable solution.
A.
