Processing Orders Through Shopify, Can It Be Done?

This might seem like a silly question, but I actually saw it being done previously (but not on CS-Cart).

Can we process the checkout part of the orders through Shopify?

The reason I ask is that non of the Payment Gateways that integrate with CS-Cart work in my country (Qatar). However, in shopify I am able to use a couple of gateways for the country.

So is there a way I can still have my CS-Cart website up and running, but when client clicks checkout to process the payment it would be handled by shopify?