I would hope that you're throwing a STAINLESS STEEL Remington into the dishwasher. A regular blued steel gun would, I'm certain, be rustier than the hinges of Hell.
I suppose if you pulled it out immediateliy after the washing cycle, then rinsed it in hot water, followed by an air-blowing and oiling, you might get by.
I'd rather just clean it with hot, soapy water as I've been doing for about 40 years.
But I don't detail strip my revolvers like I once did. Living in the Utah desert, where humidity is generally low, lets me get by without detailing each time. If I lived in Seattle, as I once did, humidity there would probably mandate a thorough cleaning each time.
I remove the nipples, thoroughly clean the cylinder, clean the nipples, clean the bore and use a damp rag to swab around the frame and hammer. Pay particular attention to the hammer channel in the frame, which can get a lot of crud. I use Q-tips to get down in there.
Eventually, the action gets balky so a detailed cleaning is necessary. I almost never find a spent cap in the innards of my Colts, because I've adopted a practice of turning the revolver upside down while I cock it, all the while keeping the pistol pointed downrange.