Sure if you replace the 10s cogset with a shimano/sram 9s one.
Swapping cogsets each time I want to use the trainer is not a viable solution for me. Too much work, especially considering I'd be doing it every week.
But, I think I found an answer, another PowerTap! I decided to get a used PowerTap wheel to use on my indoor trainer. After some searching, I found one on Ebay. The price was right and it will allow me to have an extra wheel if I need it. The PowerTap is a few years old but works fine. It should be a perfect solution, allowing me to keep my old 9-speed setup to use on the trainer and outside if needed.