I really think it depends on the rpers.
That's pretty much it, yes. Everyone has different rules on this topic; some will not allow you to even touch their character, while others can go as far as to let them speak and act the way it most fits the situation. Overall though, I'd say most people are fine with just saying that their character is tagging along yours, as long as you don't have too much dialogue or big events happen.
But yeah, you can find out your partner's exact personal preference with a simple question, so that's what you should do.