The sill overhang will all but weather a dwarf wall.
I can not see where water will be getting in.
There is no sill overhang on the outside of the conservatory its flush with the brickwork on the dwarf wall. The dwarf wall is one course brick, one course breeze block no gap and then the stone lintel sat on the top so no overhang on either inside or out and then on the inside is a plasterboaed with a foam backing attached to the breeze block