I've had a second look at the published scheme and it does say "a new green byway". So it does seem that the tarmac will be ripped up. Here's the relevant parts of the scheme:

"Between Longbarrow Crossroads and King Barrow Ridge, a new green byway would be created, generally following the line of the existing A303. The byway would provide a route across this part of the WHS for non- motorised users who would be prohibited from using the tunnel. The byway would link with existing Rights of Way in the area."
".....the existing A303 causeway restored to historic turnpike levels."

So there will still be a road on the surface.