I run the breach before filling. The breach lines (usually the agreestream lines for me) basically make hole in the walls that you may have created (built). I don't think they breach or lower the DEM. If you are using tools other than the Arc Hydro tools (I'm still in Desktop version) the process you would follow might be different.
In the Arc Hydro workflow and tools, the Breach line is chosen in the "Build Walls" dialog box.
If I were given the same task, and using Arc Hydro, I would definitely add an agreestream (Arc Hydro default name) polyline right where road embankments begin to raise the streams up on either side fo the culvert or bridges (basically connect the thalweg of the stream I see on each side of the embankment). Other major infrastructure (bypass pipes, etc.) could also be burned in. A wall could be created wherever there is a long low feature that the DEM doesn't define a linear rise (railroad embankment for example) and the breach line (again I usually use the agreestream) would breach this wall when the processes are run.
If you have a dam that you want to define the stream through, simply putting a agreestream line through the dam will do the job of "breaching" the dam. There would be no need to build a wall at the top of the dam (unless the DEM cells are large and the dam embankment is "fuzzily" defined).
When that is done, the next step is to fill the sinks.
I look for places to put breach lines by running the process through the fill stage and then doing the raster math to surtracted the rawdem raster from the fil raster. This shows me where things were filled and usually shows "flooding" behind embankments so I can know where to burn the streams through them.
If you have a large DEM grid size and steep canyon walls, burning through road bridges and culverts may not be nessesary.
Hope this helps. Feel free to ask for clarifications.
Mark
