Prison guard: See you soon, Ray.
Ray Merrimen: No you won't. (00:36:55)
Ray Merrimen: I ain't cuffin' up.
Big Nick: That's OK. I don't bring my cuffs anyway. (01:34:05)
Ray Merrimen: Get to know your enemy, boys. (00:22:45)
Ray Merrimen: We're cop killers now. (00:09:30)
Answer: Considering how microwave ovens work, it seems it would. Microwaves work by bombarding whatever is inside with actual 'microwaves' which works to excite the water molecules within. Paper, and in the case of cash, cotton, wouldn't be affected on its own but the water inside would be. Ever had something wrapped in a paper towel when you microwave it? The cash is not metal, and the water content is what gets heated up inside and evaporated, so I believe it would work.
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