Unfortunately, nobody knows for sure how it's going to work for FFXIV expansions. SE hasn't released any specific information about it.*
All we've got are educated guesses, which could go either way. With XI, you only needed one license key per account, regardless of platforms (as long as you could install the software). But that applied to the game itself in XI, too, while with XIV, you need one license key per account per platform for the game itself. So pick your interpretation and place your bets.
*And frankly, if they did, it would probably be worded/translated in such a way that it wouldn't actually clear anything up.