I am looking at ways to improve our position in Google Products and considering enabling Google Checkout as a means to do that since customer reviews are crucial for ranking on this medium, and you can't have customer reviews appear there unless Google Checkout is enabled.
The only problem is that we have an Ecommerce store with order numbers, so any order that is placed through a third-party site like Google Checkout would need to be reflected automatically into our Ecommerce store for the greatest efficiency. Is this possible? If not, I'm afraid we're not going to be able to enable the feature, which means we won't be able to compete with all those other entries that have reviews and starred ratings.
Although old post, from my experience depends on the cart. You should be able to do level-2 integration with GC and so you can update the orders as the google server notifies you of the order progress. The concept is the same with all the popular payment processors where the client needs to login externally. Paypal instant payment has a similar process.