The short answer is no.
Unless shop.com is providing payment services, this is probably a rather inappropriate way to manage shop.com services.
A checkout success module might be more helpful, but it only offers one shot at processing and if your payment is not complete posting to shop.com may not be a good thing.
If you want to take that chance, the shipwire module may be the start for which you are looking.
If you would like to implement something more robust, this would be an opportunity to work with the Eos development team as we have some plans in that direction which would fit well with your needs.
David