Explicit IDs
If you explicitly set the document ID when indexing, nothing prevents you from using the same ID twice for documents going in different indices.
Autogenerated IDs
If you don't set the ID when indexing, ES will generate one before storing the document.
According to the code, the ID is securely generated from a random number, the host MAC address and the current timestamp in ms. Additional work is done to ensure that the timestamp (and thus the ID sequence) increases monotonically.
To generate the same ID, when the JVM starts a specific random number has to be picked and the document ID must be generated in a specific moment with sub-millisecond precision. So while the chance exists, it's so small that I wouldn't care about it. (just like I wouldn't care about collisions when using an hash function to check file integrity)
Final note: as a code comment notes, the implementation is opaque and could change at any time, so what I wrote might not hold true in future versions.