I would guess not.
I mean, you already clearly have access to the Internet as you are using it to call the API, presumably you have the ability to search too.
The difference between search and, say, document retrieval or running a Python environment is that OpenAI doesn’t need to call any other external APIs to do those. In order to search, they need to call an external API.
That said, who knows… maybe the same time they launch SearchGPT they’ll include it in the API or something like it.