Before I switched to a different agent, I routinely ran into situations where I would say "write a plan to do x", it would start planning, and I would steer it by saying something like "update such and such a file, instead of other-file" and it would immediately update it, even though it was in plan mode.

Then I would point out "you're in plan mode, don't update files", and it would go absolutely ham undoing changes and furiously apologizing "You're right! I'm in plan mode, let me undo those changes I wasn't supposed to make!" - meaning that now it's broken the rules twice.

Plan mode does not disable any writing tools, it just changes the system prompt, judging by my experience anyway.