Its fine – I live in Billingshurst, so ride bits of it regularly.
The worst bit on that route is Bury Hill, which is quite an unpleasant climb heading south. It’s two lanes, so you shouldn’t have too many problems with cars, although it is fast. I’d recommend going up from Amberley – turn left at the foot of Bury hill, then right and right again broadly. Much nicer climb, with far fewer cars.
You’ll not get as far as Fontwell – you turn left at Whiteways and drop into Arundel, nice descent. I’d ignore the signs for Littlehampton but turn right at Arundel towards Ford – past the prison, then turn left and into Littlehampton past the station.
Probably nicer on back roads it must be said.