Ran a test checkout on one of my client's sites today from Google Checkout. The transaction processed smoothly on Google and receipts were received quickly, however, the transaction was never given back to the site itself. The order never appeared on the site, and in fact, it also failed to clear the shopping cart. When I returned to the site after confirming the purchase with Google, the shopping cart still had the item in it.
This was done as a live purchase, not in the sandbox.