Mpfou, in some cases it is possible if the pancreas becomes involved, and you're experiencing true fat malabsoprtion.
But if you're talking about food 'seeming to run through you' that could be due to bile 'dumping' - non-regulation of bile release following gallbladder surgery. It causes fast transit of material through the GI tract and diarrhea.
Do you still have your gallbladder?
You mentioned that sludge could lodge itself into the bile duct...could this cause malubsorbtion and diareah?
It's possible you might be able to try some stone dissolving medications, but you'd have to check with your doc to see if you're a candidate for those type of meds. Sludge can cause a myriad of problems such as moving into the common bile duct and 'lodging,' or moving through the biliary system and irritating the sphincter of Oddi - the muscular opening to the duodenum and that can cause a lot of pain and long-term issues.