Is it possible to use something like dropzone.js for file uploads with sprout forms?
You will have to upload the files and index them as assets, then return the asset id's to your form. You can then use these asset id's in your form so you can post them to the server, effectively creating the relations you want.

I've put up a little gist that does this for jQuery File Upload - you can use it as a reference for any other upload mechanisms: https://gist.github.com/boboldehampsink/2e645655d613574ec4b7