Does ripening banans in a bag with other fruit harm the other fruit? Our office just got its first fruit shipment, which included an apology for the under-ripe bananas and the suggestion to put them in a brown paper bag along with an apple to speed up the ripening.  Does doing this harm the apple?

I'm aware of Why does a brown paper bag speed ripening?, which talks about why this works, but the focus there is on what's happening to the ripening fruit, not what happens to the catalyst.  We want to know if using one of the high-quality apples they sent us would lead to regrets.

By browsing this site I've learned that there are other ways to ripen them, including apparently just putting them in the bag without the apple.  The instructions from the vendor made me curious about the apple, though, so that's the focus of this question.

(If you make alternate suggestions, please bear in mind that we're in an office with limited kitchen facilities.)
It doesn't harm the apple, but it does speed up its ripening as well. And that risks over-ripening. So your perfectly crispy apples may begin to become mealy. Eventually they become targets for yeasts, molds, etc and start to rot. But it's not making them toxic or causing untoward chemical changes. They're all just speeding each other up.

Yes, you can just put them in a bag without the apple. They will produce their own ethylene (the gas that causes ripening, and which they make while ripening). It may take longer, since under-ripe bananas will put out less ethylene than a ripe apple, but just by a day or two. It's just a question of how hungry you are.