You can also get Quetzecoatl and Shiva from the classroom computer, and that would suggest they can exist as energy, perhaps electricity in this case.

They can certainly be contained as Diablos was. I doubt the cursed lamp was the same size as he was. And Bahamut was in the blue core at DSRC.

Other GFs seem to exist mainly in material form, like Ifrit or Brothers.

Another point is they are summons which means most of time they do not appear unless called on by a junctioned character.

So that would suggest that GF's can easily shift between coporeal and noncopreal forms.

Ultima and Omega seem to behave like Bahamut, exisiting primarily as energy and materializing only to fight.