The docs all say there is a time and billing cost:
> Auto mode may have a small impact on token consumption, cost, and latency for tool calls. https://claude.com/resources/articles/auto-mode#what-to-expe...
https://code.claude.com/docs/en/permission-modes#cost-and-la... doesn't say anything specific. It mentions that server-side classification can be used but doesn't talk about the billing for it.
But at the end of the day it is a leaky system. It may reduce the frequency of bad actions but doesn't prevent it. So you need the sandbox either way.