The actual death itself isnt really a suicide per say. If he is killed in battle whilst performing at his best (ie not taking active measures to clearly ensure his death) the exact event of when he is precisely killed if ever is not privy to him, and thus he isnt the direct author of his own demise. However he clearly has a generalised suicidal thoughts and plans, but i would rather categorise him as having self-destructive behaviour, somewhat similar to the hopeless alcoholic drinking himself to the grave.
I think suicide is characterised by that action immediately prior to death which is clearly the direct cause of ones own demise in so far as without that specific action, the death wouldnt have occurred. So acting whole heartedly in a manner of self preservation within a war and to be killed by another is out of your control by definition, so it isnt strictly a suicide.