No. I began buying the FF14 blu-ray soundtrack albums via Amazon a couple months back, just finished the 5.0 Shadowbringers album today. When you open the plastic packaging, there is a piece of cardboard wrapped around the corner of the case. The cardboard for the first four albums (1.0 Before Meteor, 2.0 A Realm Reborn, 2.5 Before the Fall, and 3.0 Heavensward) does not have any numeric codes on them. It's just Japanese text. Starting with the 3.55 Far Edge of Fate album, the cardboard slip does have numeric codes that you can enter onto mogstation to redeem the minions.

I have heard on reddit that some people who had older blu-rays that had the numeric codes printed on their carboard slips were able to redeem the minions after the "expiration date", but my guess that the likelihood of you being able to obtain codes printed from that long ago are very low.