Do you know of an evergreen groundcover that grows fast and will flow down a wall?

yes the junipers will work very well, I would recomend The variety 'BLUE PACFIC' it is dwarf in height only gets 1' tall and spreads to 5' wide and will trail down the wall on it on. This type will not give the carpet look it gives a more viney appearence, for a carpet look use variety 'BLUR RUG' grows to 4" and give the solid flat carpet look I would rate neither of these as fast growers but I think they will fit the bill for what your want there.