Matching GTFS with OSM PT/bus route relations?

I’ve played around a lot with public transit routing. My use case here requires seeing the actual path that the vehicle takes rather than just where the stops are.

I’ve tried converting PT output to GPX and then feeding it to the map matching module. Obviously this may not be accurate and underground metros will just break since it will try to match the surface road. Without some input/output surgery, it will also break the walking part of the trip.

Now I noticed that OSM does provide bus route in the form of relations and it shows the almost exact road segments taken to a certain extent.

Has anyone ever dipped into this matter? Is it possible for GH to use this information to pair with GTFS files?