The SB1 action will not take it as I understand it, and I don't think it is convertable to centerfire if it could. But that barrel can be fitted to an SB2 (centerfire) action, no firing pin work.
On another board a guy did a 17 hmr to 17 rem but the fit to the action is key, he never got it to fit right so accuracy was not good, he sold that barrel off to another guy but I lost track of it after that. I know of one other similar conversion but it was 22 mag to 218 bee, last I saw that one had turned out good. The lock up needs to be about .0015" but no more that .003" and even there accuracy is so-so.
The ejector spring is not as strong in the rimfires and you will probably have to dremmel the ejector as well, I don't think that a standard hornet ejector can fit in a rimfire barrel lug. It would be an interesting gun if it worked out.