Hi @ptrwlr,
As I was just told by a colleague, it is possible after all. You can use knime://knime.node URLs to reference the folder of the current node. If you add a file to your component, using such a URL you are able to read it. Everyday I learn something new about KNIME 
Kind regards,
Alexander
Edit: It seems like while this works for components, all data is removed from the component folder when you share it. So for your use case it might not be good enough 
Another edit: We do have another ticket already and it is in the backlog. So maybe the feature will be here soon for shared components.