I just had a look, and they don't. It's really just a temporary fork of the conversation, so it's fully cached. But it does run every 30 seconds, so that is very bad especially if it's a subagent that's at 800k tokens.

And I don't really get the point of this feature, I've always found it super annoying that the main agent creates a subagent with the clear description of "Fix tile cache" for example, and then after a while it turns into something generic like "Running browser tests"