Not really, Cindi. I am not 100% certain this method will work for your one-cane wonders, but instead of hoping they survive the winter, why not try an experiment ? If you have a place to put canned roses where they have winter protection, I suggest you dig them up and put them into a container and allow them to grow roots. This may stimulate them to put up new basals, too.
Since I have never gardened in your climate, this is only a guess on my part. However, one of the lessons I have learned from the roses during my rose life is that I learn more about why a rose is failing when I look at the roots than just observing it's top growth. If you really think you are going to lose the rose, why not experiment ?
