The car is actually the car Honda started designing half way through last season. When Ross Brawn joined Honda the team was in a bit of a sorry state. The car was useless and they were chasing their tales trying to make it faster. Ross Brawn convinced Honda to halt all development on the 2008 car and concentrate all their efforts on the 2009 car. So from half way on through last season Jenson Button's Honda received absolutely no development what so ever. That's why it got progressively worse and worse.
So in short, Honda pretty much already knew they had a potential world championship winning car before they pulled out of F1. However the decision had already been taken. Ross Brawn, and pretty much everyone else in the team (Nick Fry especially) also knew the car's potential, that's the main reason they committed to the purchase of the team.
There is a rumour that Ross Brawn actually paid $1 for the team, and Honda gave him £40 million (what they would have had to pay it's employees in severance pay), so he could conceivably run the team halfway through the first season without the need for a sponsor.
Honda have more to do with Brawn's success than you might think.
*edit* Here's the weights for the start. Unusually it seems the Brawns are running light.
1. Jenson Button, Brawn GP, 646kg
2. Sebastian Vettel, Red Bull, 651.5
3. Rubens Barrichello, Brawn GP, 649.5
4. Felipe Massa, Ferrari, 655
5. Mark Webber, Red Bull, 651.5
6. Timo Glock, Toyota, 646.5
7. Jarno Trulli, Toyota, 655.5
8. Fernando Alonso, Renault, 645
9. Nico Rosberg, Williams, 668
10. Robert Kubica, BMW Sauber, 660
11. Kazuki Nakajima, Williams, 676.6
12. Nelson Piquet, Renault, 677.4
13. Nick Heidfeld, BMW Sauber, 676.3
14. Lewis Hamilton, McLaren, 683
15. Sebastien Buemi, Toro Rosso, 678
16. Kimi Raikkonen, Ferrari, 673
17. Sebastien Bourdais, Toro Rosso, 669
18. Heikki Kovalainen, McLaren, 657
19. Adrian Sutil, Force India, 675
20. Giancarlo Fisichella, Force India, 656