The only way to know for sure is to try it, making sure it's completely dry before doing so. Personally, I think it will, but that's really just a guess. If you do try it, please post your results here.
I've definitely washed my Magstripe reader on accident as well and mine still worked after letting it dry. Like @GlassJudy said, the only way to know is to try. 🙂
