You are right, Simple Sharing goes through to Samsung's servers if the file is too large for MMS or the recepient's phone doesn't support Simple Sharing.
I just tried it to my work phone and when sharing the image I do see the expiration date set for tomorrow on my phone, and when I get the link, it also says it expires tomorrow. If you go to the contact you sent something to you should see a history of the messages sent; there I see the message sent to my work phone and the text body also states 5/5 as the expiration date.
UPDATE: Apparently also in the Contact's information there should be a Simple Sharing entry with the stated expiration date. If you tap that one it takes you to a screen where you can further see all sharing history, and that should list all shared files with their corresponding expiration dates.