Selection issues, board politics and coaching controversies including Jake White's most recent public row continue to plague the game in South Africa.
However, Connolly believes the Springboks are strong enough to cope.
"I don't think they'll implode," he told the Daily Telegraph.
"They've got a lot of national pride, pretty good structures in place, a lot of depth.
"They've got each position covered a couple of times and that's a big help for a coach.
"South African rugby is in a pretty good space at the moment, just like the Kiwis are.
"To get two teams into the final, win a Super 14 and to have the depth they have across the board... it was always going to come, you thought, with South Africa and it's nearly arrived with the depth they've got and the quality of their play.
"They're a good team. Whoever comes here finds it very hard to beat them at home."
Wallabies lock Nathan Sharpe, who has one of the most difficult match-ups against the formidable Springboks second row of lineout legend Victor Matfield and Bakkies Botha, admits the battle in the forwards will determine the outcome of the contest.
"They are attacking wide once they do get a bit of ascendancy up front. So we need to stem that play from them," said Sharpe.
"If we can control their momentum up front and our defensive system is tried and true - if we can execute our tackles well - then I think that it's going to be a lot tougher game than people are expecting.
"The Springboks are very good at the set-pieces - scrummaging, mauling, lineouts. That's always an area they're strong in so we need to be on top of our game there."