Not really. The Aus series was more or less determined by the fractious Sydney Test Match. And Kumble was inspirational in that with his bowling. Moreover, Dhoni wasnt ready for Test captaincy yet.
The problem for Kumble started when he started failing with the ball, The SA series was seen as just a low, and he missed the last test owing to injury. Dhoni won that match, but that was really a here-or-there pitch. The real low came in Sri Lanka, where, inspite of having the most experienced duo of spinners, India still lost the rubber. I think by that time, Dhoni had finished his apprenticeship and was ideal time to assume captaincy.
However Kumble would have sincerely thought he'd have a last hurrah at the Aussies. I think Kumble delayed it by a series, his retirement. But being the champ he was, he could take that.
If India had brought in Amit Mishra at the start of the series itself, perhaps we'd have won it 3-0.