I wouldn't worry about if he gets the rewards or not, but I'd be more concerned with if you kick him and he can't participate, how does that affect your war? Do his teams get removed, leaving spaces in your zones or do they stay? Would this person have attacked, and without him you lose a few teams from your offense?
If you don't have that information, I'd almost suggest booting him at the end of the war (when you know if you will win or lose) or after it's over, just to ensure you don't lose over booting someone.
Good news is at least they participated to some degree. We just did a purge of several people who continually don't help out with guild events while accepting the rewards. Feels nice to be rid of the dead weight.