unlikely, Harald H invaded to take the kingship for himself, on a very weak claim. having killed the King, I can't see him making Tostig King instead, that wasn't in his character. Harald would want to be King of England-he might make Tostig his right hand man in England.
Regarding Southern England, do remember that the Normans were unpopular there-Edward's 'norman' favourites did a good job of annoying the locals and after the Dover incident almost started a civil war. With Edgar Atheling in London (and with a good claim to the throne), he could rally a defence against William and without the need to rush to engage him in battle, a full fyrd could be summoned and who knows, it could do William a lot of damage and perhaps beat him. Even if Edgar doesn't end up King himself, I suspect there would be a lot of nobles in the South who would take Harald over William.
As to fortifications, whether the Norse had such a tradition or not, there was a long one in England. Putting aside Burghs, there were "fortified Thegnly Residences" (very much like ringwork castles).