Hi,
It's possible DGN files might be viewable in Explorer if added as a Layer File (this means creating the Layer File in ArcMap). Alternatively, as you suggest, another approach would be to create a GP service which takes a DGN file and returns some form of Layer - I'd suggest a Layer Package because then you could define the rendering for the data to view in Explorer. Perhaps it's possible to import the rendering from the DGN file itself? (I'm not familiar with the technical implementation of that format).
Regards
Mike