This capability is very possible, however you could not achieve it with a website alone -
to offer an offline-usable webshop service you would need to create a standalone mobile application for your target mobile/tablet operating systems (for example: iOS, Android), and then get those who would need the offline capability to install this app onto their device.
When embarking on the mobile app development project you would need to use the following user stories as a minimum functional requirement:
While offline (no Internet available):
(a) The app would keep a stored copy of the entire product catalogue on the mobile device enabling the creating and editing of orders in full, but without stock quantity checking.
(b) Orders could be committed/confirmed but then would essentially sit in a queue waiting to be submitted when the device is next online.
(c) A copy of all existing submitted orders that are in progress would be kept stored on the device for easy/quick reference.
While online (connected to the Internet via WiFi or GPRS/3G/4G etc):
(a) The app would download the latest incremental updates to the product catalogue to ensure it is up-to-date.
(b) The app would download information about any existing in-progress orders associated with the user that may not currently be stored on the device, for example they may have been ordered over the phone or via the website.
(c) For each completed order waiting in the queue to be submitted:
Check that any products chosen in each order still exist in the updated product catalogue, and if not mark that selected product as discontinued in the order, and notify the user with an alert or some kind so that they can make an alternative selection.
Check that sufficient stock is available for the product quantities selected, and if not mark that selected product as out-of-stock or limited-stock, and notify the user with an alert of some kind so that they can make an alternative selection.
Submit the order and mark the order as submitted, removing it from the queue.
Take payment for all orders awaiting payment if appropriate, depending on your business requirements this step might just involve sending a PDF invoice by email to the user with information about how to pay and the payment due date.
(d) Check for any new messages that have been added by staff to existing orders and notify the user with an alert of some kind so that they can read the message and become aware of any delays or problems ASAP.
And in order for this to be possible the current webshop would need to undergo further development to include an API with which the mobile app could communicate.