It's an edge case.

Is what the user doing on sub A against the rules of sub B and C as well?

Can it be reasonably assumed the user won't stop doing what got them banned from sub A?

Is the user a participant of sub B and C?

If the answer to all these is unequivocally yes then you can choose to deny them access from your related subreddits since it can be argued that you shouldn't need to wait on something you know will likely happen anyway.

But, if you think that the ban on subreddit A means they learned not to do same on sub B and C then it becomes less clear-cut.

I'd judge this on a case by case basis and I'd be hesitant to pull that trigger, unless what they did is really beyond the pale.

A better criterion would be: Is the user already breaking rules in sub B and C?