Hmm, yes. But only if we assume that:
Odin - Lightning elemental
Shiva - Ice elemental
Brynhildr - Fire elemental
Bahamut - Non-Elemental
Alexander - Holy
However, I'm thinking about how Bahamut looks and the color scheme he has, which is black/purple. Do we really know Bahamut's affinity? My point is, Odin, who is traditionally non-elemental, seems to have been changed to lightning elemental this time around; so couldn't that mean that Bahamut has changed as well?
If my theory proves correct, Bahamut has a darkness affinity this time around and the final one is non-elemental. Vanille's name might suggest it, too, since Lightning has Odin and Snow has Shiva. Vanille's could be a "vanilla summon", as in an/a "as is/neutral" one.
The new list would be:
Odin - Lightning elemental
Shiva - Ice elemental
Brynhildr - Fire elemental
Bahamut - Darkness
Alexander - Holy
???? - Non-Elemental
But I'm probably just getting carried away conspiring. :lol
Edit: The final one could also be water, as duckroll? suggested. But only if it's about balancing out rather than "fitting summon for char x".