Yes, they can! But only if you give them your log in and password. (You can change the password afterward, if needed).
Once they log into My Account and click on Continue project, they will click on the ART section.
If they want to upload the native files, they can click on Advanced Graphic Services. There is a nominal fee for this service.
Otherwise, they can click on Upload Finished Artwork (PDFs), download the proper templates and then upload the exported PDF files (with template guides removed).