Maybe not 'ash' in the oil.
But reports after volcanic ash encounters (eg. the NASA DC-8 Incident in 2000) include references to very high levels of SULPHUR in the oil. This was taken as a confirmation that the aircraft had indeed gone through an ash plume. Sensors that happened to be on the aircraft also recorded high levels of SO2 in the outside air - so that's the route by which the sulphur gets into the oil.