No, you mentioned that the only reason he was made General was that he was a Muslim.
"And Khalid Bin Waleed was only made general after he accepted Islam. Not while he was a pagan!"
I think it is fair to assume that Muhammad was a man of above average intelligence even by today's standards. He allowed Pagan prisoners of war to teach Muslim children - if they are qualified to - for their freedom. I think he would have no problem employing pagans in the army if he saw a benefit in it for Muslims.
Many scientists during Islamic Golden Age were rationalists and did not believe in Quran, but they were allowed to work in high engineering positions and make weapons of war for Muslim armies.