It does have the ability to. You need to have them email your Updox Email from outside of the portal (ie using their gmail, yahoo etc.).
To find your email address to give them, open the Updox Workspace > Admin > Manage Users > scroll down a little to find your Updox Email (Not your NHIN Direct Email, idk what that exists for bc it doesn't work). The address should be yourname@myupdox.com.
They can use their email client (gmail, etc.) to send you attachments just as they would using normal email. I've tried with PDF and JPG attachments and they both work. They come into your updox inbox in color too.
I'm not sure why this functionality is not available in the portal accounts (yet?) but the patient doesn't even need to have a portal anyways.