No it won't, but it wouldn't get any worse either. He probably has to live with it.
This. I find alot of my good FMs have at least one trait or ancilliary that is detrimental to the job they are doing... You clearly can't roleplay both warmonger and war weary at the same time, so I say just roleplay the one that came first, as, it could be argued, this is going to be the one that is more deeply in-grained in his personality, the one that is more "like him"...