Definitely not - or some it for sure. It's fast and dangerous and not very wide after Charleston.
There's a good cycle path from the roundabout south of the Cuifail tunnel, alongside the A27 for a few miles. Then you are best advised to cut inland on Burgh Lane, and wiggle thru the lanes - Firlelane, Langtye Lane, Lwr Wick St, Stationrd and back to the A27.
Then you're buggered and would have to dice with death to Polegate, or head south and flog up and over Cuckmere, East Dean and Beachy Head on the A259.
Or get a train from Berwick Station.
I've gone Ringmer - Laughton - Golden Cross (where it gets a bit shoot on the A22) - Hailsham - Stone Cross when visiting mates in Hampden Park
glynde - upper dicker and then legged it over the A22DC and into Hailsham
If you need to take the direct route between Lewes and Eastbourne, there must be a urgent need, if that the case use the train. If there is no hurry or urgency, then head north and wiggle your way through the back lanes to Hailsham, then down to Eastbourne.
No, but, you can cycle from Brighton to the east side of Seaford without actually doing more than a short section on the main road. Then a pretty diversion via Birling gap and Beachy Head and you can roll down into E'bourne on the beautifully named Paradise Drive!