A dual carriageway would be highly visible in the landscape as well as noisier than the present road. An off-line single or dual carriageway new road as preferred by some politicians would also be highly intrusive at this point.
The Government has allocated around £70 million to address safety and capacity issues on the A27 between Lewes and Polegate. Highways England has drawn up plans for these improvements and announced its preferred option some time ago. These should be being progressed now and an announcement is expected in early 2019 as to the way forward.
These sorts of measures are unlikely to have a significant impact on the National Park and could lead to improved access by walkers and cyclists into the park (across the A27).
However, the situation is confused by the parallel on-going lobby by some politicians for a brand new A27 between Lewes and Polegate which could cost up to £1 billion.