Verified answer

Exp. Share does not harm your Pokemon, happiness can increase while holding it even if it doesn't battle. likewise, it will gain EV's (its stat points will increase like a Pokemon that battled and leveled up). The only thing you can do to effect the EV levels (stat points) in a negative way is to give the Pokemon rare candy before they get their effort ribbon (after you get the effort ribbon the Pokemon has all the EV's it can possibly get).