Regular claude code is already a remote access door to your setup, once you've granted a few command execution permissions. (e.g. if it can edit your code and run the test suite)

Yes and no: I hope (not verified) that regular claude code client only sends requests, and doesn't open ports for remote access

I wouldn't expect Remote Control to open any ports either

There's nothing stopping CC from spinning up a local service or running terminal commands to open ports.