Despite being in a relationship they outwardly protest, Ranma and Akane are very supportive of one another. Whether it's patching each other up after a fight, sacrificing a chance at a cure to come to the other's rescue, or eating toxic cooking just so the other won't be sad. Even when they're sad and depressed, they have each other's backs - be it due to moving, struggling to learn a new tehnique, or having trouble against a strong opponent - they always worry about the other, and go out of their way to try and cheer them up.

There are entire story arcs that begin with a simple desire to support the other. Ranma joins the cheerleading competition because he's angry that Akane's opponents made her cry. Akane supports Ranma during his hiryu-shoten-ha training by helping him bring out the "fire" he desperately needs, and again, when she sees his moxibustion chart get swept up in his tornado-attack.

If they legitimitally didn't care about the engagement, there's no reason they'd go so far out of their way to help.