Eventually, yes. Although, time seems to feel differently while you're there and when you leave.

[He's pretty sure it's some type of time dilation, but that's hardly something he can go spouting to a newcomer. Not many people in his acquaintance back home would understand that, so he's not going to overwhelm a stranger.]

How about I come and find you? If you stand by the area in front of the board with the rideable birds called Chocobos, I will be able to find you. You will know it is me when I arrive.

[Besides, he can fly and he's made his way through the Gold Saucer already, so he's got some idea of what he's doing by this point.]