Without Phoenix's hack it doesn't work properly, it doesn't get added to the list, it is displayed after battle though:

I should have specified that I meant with the hack. Even if you add it to Rydia's unused summon learning list, which
should work, it won't work without the hack.
Phoenix: Spells from the third slot only get added to the third, spells from the second slot are added to the second and third, and spells from the first at added to all three.