AFAIK semi-pure carbon like charcoal or biochar is not biodegradable or extremely difficult to biodegrade. See here and here and here. Burying such carbon rich solids in soil would result in carbon sequestration.
My hometown is located on a plain with lots of > 2 meter long grass. Now its an El Nino and almost summer time so the grass is dry and fires often occur. At this time of the year, I can often see black biochar on the ground from dry grass fires. The updrafts from the fire lift it up and the wind carries it for kilometers. You can still see the fine structure of the leaf on it. But it crumbles into black dust if you touch it. Step on it and it mixes with the soil. You probably have carbon sequestration right there. This reminded me of the grey soot from all the diesel jeepneys when I used to live in Manila. It collects quickly on exposed surfaces and clogs up my PC's air filters. Its a little better now that air quality laws were passed.
Like diesel, biodiesel also causes some carbon particulates which end up as dust and soot in the air. Some of it lands on the soil or on the sea and might be incorporated into the soil or as sea sediments. If that happens, then its a form of carbon sequestrations. Biodiesel should be carbon neutral but this might force biodiesel into carbon-negative territory.
UPDATE: of course since modern diesle engines produce little soot, the sequestration effect is very small compared to say using diesel to actually MAKE biochar in a dedicated machine then burying the biochar in the ground.