I'm not sure if you know, but they had shared subscriptions when FFXIV was released, I have the link here, it offered a discount if you purchased both
http://www.playonline.com/ff11eu/topics/ffxiv/
They stopped it, I think when FFXIV got canned for ARR, maybe before.
While I probably wouldn't use it, as I never got on with FFXIV, of course I would support it, FFXI would be the main beneficiary, bringing more people back who have jumped ship.
I remember way back, when they were developing FFXIV (Or Rapture as it was known), there was some talk of linking the games, so you could chat between them, but they never went through with this, shame....