I'd be real leary of that. Dishwasher soap can really do a number on stuff that isn't made for a dishwasher. It can remove or destroy a fine finish very quickly.
Just make certain the OL will be gone for an hour or so. Also, don't use sink-type, like Dawn, dish washing soap. It suds like a SOB and will get all over the kitchen floor, taking, at least, an hour to remove the evidence (your kitchen floor will be cleaner than when she left, raising questions). Use regular dishwasher soap designed for China, if you feel soap is necessary. http://www.getdecorating.com/design_...eID=390&page=1
If the OL asks, this is not my wheel, nor our dishwasher:
Nevrdull is decent stuff but I've found it can leave small abrasions in the chrome. Wizards is another product I've used for a year+ and it works amazingly. Get yourself some good microfiber cloths and you're set!