Could a kerosene fueled jet engine run on methanol without significant modifications?
You couldn't have any aluminum components in the fuel system because methanol dissolves aluminum (F1 race cars remove and purge their fuel systems right after racing).  Ethanol would be much better in that regard.

It would take changes to the fuel controller to change the air/fuel ratios used with less energy density.

Other than that, I don't think it would be a big problem.  I've been told that the Honeywell/Lycoming turboshaft in the M1 Abrams tank will run just about on any liquid hydrocarbon.. gasoline, kerosene, diesel, booze, rubbing alcohol...