[jpn of Seattle]

Belle asks: "does globalization depend on oil?"

Wikipedia defines globalization thus: Globalization (or globalisation) is a modern term used to describe the changes in societies and the world economy that result from dramatically increased international trade and cultural exchange.

I imagine oil will just get more and more expensive, and be gradually replaced with alternatives as they become more economic.
I doubt this process will have Draconian effects on international trade and cultural exchanges, other than making them somewhat more expensive.

I have little doubt that the world will just keep getting smaller and smaller as our communications technology gets better and better.