I have tried using the dissolve tool with unsplit_lines option but it does not merge the lines... maybe there is a step I am missing?
You could convert you dgn layer into ar feature dataset and create a topology to bridge the road gaps. You must have either ArcEditor or ArcInfo license level to create topologies. After you are comfortable doing this you could create a model using the topology geoprocessing tools to automate the process. Once you have the model set you can export it out to a python script.