I'm sure a lot of people would. It would be nice to turn the bit into something positive. I agree, that at this point, it would be the only way to justify the episode. Like @grudlian.said, you don't want to set a dangerous (i.e. obnoxious) precedent, but if you turned it into an event (and make it clear that this is a one time deal), then why not? You can maybe even set it up as an auction. Like they will only do an episode if they reach a certain dollar amount which will be donated to the charity of their choice.
I don't want to speak for them, but honestly, I think this would be a pretty cool idea.