According to modal logic, yes. For God is defined here as a necessary being and necessary beings exist in every possible world if they exist. So if we grant that it’s possible that God exists, then God exists in every possible world including the actual world. Note: this is not the same thing as defining God into existence because the ontological argument still requires argument for the 1st premise (the possibility premise).
On the contrary, unicorns don’t exist in every possible world if they exist in some possible world because they are contingent beings, contingent beings are beings that can fail to exist (they don’t have to exist). Same for trees, books, chairs, etc. So if a book exists in some possible world, it does not follow that it exists in every possible world.
The controversial premise, in the ontological argument for God’s existence, is rather whether it is possible that God exists. I don’t mean to say that God is somehow logically necessary, but I do think God being metaphysically necessary is up for serious debate.
A shortened version of the ontological argument is as follows:
- If it is metaphysically possible that God exists, then God exist
- It is metaphysically possible that God exist (this is controversial)
- Therefore, God exists.