I think this is such a great idea. As long as both of y'all are on the same page about your health and fitness goals and you have an open line of communication throughout then this has the potential to bring y'all even closer together.
The one thing I will say is to pay careful attention to the thin line between support and obsession. It's one thing to motivate your partner to keep going when they're having an off day, but it's another to get nuts about it. But I don't think y'all will have a problem.