Sure it is possible, I've seen some nice upload scripts out there like this one:
https://github.com/valums/file-uploader or you can investigate X-carts default file upload capabilites and see about incorporating that.
I think you may be setting yourself up for a potential security risk if you don't take proper precautions though. The file needs to be uploaded, then scanned, then moved to a safe directory. Ovious things like checking file formats, having a list of allowed formats, and limiting size are important.
BCSE also has a product image attacher, which I have used recently and it did the job. Attaches files to products though. (Is attacher even a word? I don't think so.) :_)
http://www.bcsengineering.com/store/x-cart-order_product-image-attacher.html