Hi Justin,
Thank you for giving TeamCity a chance 
In ‘Auto’ mode the SBT runner downloads latest SBT version and runs it in isolation, so no your local configs are used. In ‘custom’ mode you should provide a path to SBT installation directory located on the agents where the build will be running. SBT runner will launch ‘sbt-launch.jar’ from /bin folder under that directory. Default Java options that will be used you can see and change within SBT runner build step settings. SBT itself will use ~/.sbt directory for further configs. At the moment we don’t support running sbt with command line script but we are considering it ( http://youtrack.jetbrains.com/issue/TW-34977).
You can contact me directly at shkate at jetbrains if you have other questions.
Regards,
Kate