Using it on a company project is a great way to get going with Rails. In your case, I would say go for it, with one caveat: you (and the company) should be aware that it won't always work.
That's not a knock on you. It's just the nature of learning this sort of thing. You will break stuff, and not know how to fix it right away (other than to roll back your changes).
Learning Ruby can take a while. And when you throw Rails into the mix, you have a whole lot more to learn.
So, be realistic about it. If you and your company recognize this as an opportunity to get some production experience with a non-mission critical application, awesome! I think that's a great approach. But if they need it to be up all the time, or for you to add features quickly, then it might not be as good a fit.
But I'm all about getting paid to learn (that's all that professional software developers really do, so it's good to get in that mindset early). So in your case, I'd be looking to spin this any way I could that would get me learning Rails on company time.
Just make sure everyone shares expectations for the project. Things go wrong... and it's no fun making important decisions based on faulty data.