Is it possible to add multiple script files containing other python classes, config etc, and even .sde connection files when publishing service definition from arcmap? I do not have access to the arcgis server directories.
Yes, it is. You would need to publish a GP service (either by publishing the result directly or by saving a sd first) and this way all the data that you don't have registered as your data sources in ArcGIS Server will be published. In certain situations, I had to publish myself like that and then all the scripts required to run the tool (just make sure you import them in your script tool file) and .sde connection file was copied over (the enterprise geodatabase was not registered).