Nope, they wouldn't have - not without good fortune anyway (which they had at The Oval in 2005 with Pietersen being dropped by Warne aiming a drive at a ball that wasn't there to drive), good fortune Australia were unlikely to give them.
Some good defensive batting would easily have drawn that game, some good attacking batting was a needless risk (and something highly unlikely to have been carried-out with the skill required).
No, no, no, no, no, no, no. Test cricket is about the balance between attack and defence - ideally with a little favour on the side of defence for my money. The best cricket marries attack and defence (the best bowlers can attack and defend at the same time and the best batsmen have a range of attacking strokes and watertight defensive technique) anyway, but while the defensive aspect of the game being poor can mean the thrill aspect goes up, usually it means the quality has taken a nosedive and the true fan of the game of cricket (ie, of Test cricket) can appreciate both quality and thrill equally.
Adelaide was in its way thrilling. Little better than a game that looks like it's going for a foregone draw then gets turned on its head by something. If I was an Aussie that might be my favourite Test ever. But I'm not. So it reads pretty awfully. Australia's cricket in that match was mostly excellent, however, after being negated in the first-innings by the loss of the toss and the extreme flatness of the wicket. England's was abysmal after the first-innings - apart from the needless collapse, there was the crucial drop of Ponting by Giles.