Not a bad idea on the face of it. Its been done before, and very well. The French conquered and subdued much of their empire with the Foreign Legion and local native troops.
European officered Senegalese (just an example) would put the fear of, well, something in the hearts of the Arabs. They certainly scared the Moroccans.
The real problem is direction. If whoever was picking up the tab put the job of both organizing the army and running the war in the hands of a Hubert Lyautey or John Glubb or even David Petraeus and let him get on with the job it would be done well. The real problem is that the real leadership will be in the mishmash of an international coalition with no direction.
Sometimes things went horribly wrong. One French force's commander went Kurtz, and launched a killing spree that would have horrified Reinhard Heydricht. The French had to send another column into the interior to destroy the rogue force, which they did with heavy casualties.