Sometimes it can take longer for the payment processor (e.g. PayPal, Google Checkout, etc.) to complete their processing of the actual payment funds than it takes for the buyer to finish checkout, so in some cases there may still be a chance that the payment can fail after the buyer completes checkout.
When the buyer clicks to continue past the end of checkout, we only let them access the thank-you page for their order (including download links and any custom HTML you'd added) if we have received confirmation of completed payment by that point (which is usually the case).
However, if we have not yet been informed that the buyer's payment was completed, we would only show the buyer a generic thank-you page informing them of that fact and asking them to watch their email for further details. Once their payment is finally completed, then we would send them your thank-you email containing a link to the proper thank-you/download page for their order.
If you wish, you can allow buyers to access their order's thank-you/download page as soon as the payment processor allows them to finish checkout, regardless of their final payment status. In this case, you would assume all risk that some payments could still fail even after the buyer has already finished checkout and claimed their download. To do this, go to Seller Admin > Payment Preferences and uncheck the setting "Wait for pending payments".
Regarding Google Checkout delays in particular, the information on this help page may be relevant to your situation: