I feel like doing Strictly (if she was ever offered) and tangibly getting something out of learning dance might actually encourage her to do learn. However, it'd also be a terrible idea. As has been discussed on Tom's thread, a lot of former Strictly contestants have gone on record saying it's something you need to really weigh up doing because it can take a huge toll of your mental health and your relationships as well as physically (as AJ's injury showed). It puts you under such a microscope.
Tom seemed to struggle with the judge's criticism at times and he was a fairly competant dancer, clearly had the work ethic and is used to being in a very public eye. I don't know if Carrie would be able to handle
everyone watching her with no control over people's perceptions of her. It's not just being good at dancing, it's likability. You can only influence the audience so much in terms of what you say and do to make them root for you and as we saw in Tom's case, sometimes those attempts can backfire. She won't be able to argue with the judges or defend how much work she put into the dance compared to a tiny mistake, she can't moderate comments on every platform.
I think it'd be her worst nightmare if it isn't already