Hi @iAntis - thanks for dropping by
Absolutely - although the file structure will change slightly but your client will get used to it quickly.
In Pulse admin, there's a page called "media".
Here your client can create folders and upload PDFs, docs etc into folders and organise in the same way as now.
Then from within their site they can link to those files with the WYSIWYG editor. This is probably something a quick tutorial could show you more easily, but here are some example screens.
Add to page references:
Hope that helps! Let us know if that is what you were looking for or not