I wouldn't use it. Toxic ingredients in Irish Spring are COCAMIDOPROPYL BETAINE and D-LIMONENE which are toxic even to humans. The strong fragrance contains these ingredients and due to their sensitive respiratory systems, chickens are susceptible to the toxic effects in an enclosed space.
Besides, I have a strong hunch that the mice would overcome the strong smell and be able to determine the soap is rich in animal fat. You would be providing them a rich source of calories.
Have you heard of the bucket roller traps? They work splendidly and can catch numerous rats and mice in a single night. No spring trap to unload a dead rodent and the rodents can keep accumulating in the bucket even if you don't have time to unload the dead rodents for several days.