Yes, it does. Breadth of search is exactly what the effort setting controls.
LLM-judge/parallel branching ≠ multi-token prediction ≠ reasoning effort.
See https://developers.openai.com/cookbook/articles/openai-harmo... and src/openai/types/shared/reasoning_effort.py
I think you may be confusing the openai "pro" series models with thinking. Thos are rumored to be multi "branched"
LLM-judge/parallel branching ≠ multi-token prediction ≠ reasoning effort.
See https://developers.openai.com/cookbook/articles/openai-harmo... and src/openai/types/shared/reasoning_effort.py