Does vegetation contribute to long-term carbon sequestration?
Unlikely but theoretically possible.
As the bits of tree work their way down to the sea, they are going to oxidise and release CO2. This would appear to our eyes as "rotting" and breaking down. Leaves aren't going to make it, although they might get buried in river sediments.
Trunks might. Once they reach the open sea, they are going to have to become water logged and sink to the bottom of the sea or ocean. They are going to then have to either fall into an area of anoxic bottom waters (restricted water flow => very little oxygen if any), or be quickly buried by sediment that cuts off the oxygen.

Speaking generally, when I look at ocean sediments, I have yet to see fossil wood. I do see fossil wood in places like river deltaic sediments though (eg. the Carboniferous sandstones of West Yorkshire).