Space?!

[Kirito]

You have a point, but the Garleans are really advanced and I am sure they can find a way, especially when Van Darnus made that huge land that floated above the clouds!

I don't see the garleans deciding to let Eorzean use their ship unless there is an expansion that covers what happens after the garlean leaders are defeated and become under the control of three nations. In which case, I would expect we would get access to the empire and they could one day have an event to go to space. But those are very low likelihoods. Not so much the former since that could be a nice way to get the dark knight class unless we meet a roque garlean somewhere willing to teach the way of the dark knight.