Okay, imagine there is a Pokemon who has Water Veil up, and the other Pokemon has gotten burned. Since it got Burned, it Synchronized it, but will Water Veil prevent it from getting Burned?
It wouldn't be passed on because self-inflicted status conditions (like those from Orb hold item) aren't synchronized.
EDIT: Still, if its a normal burn, no. If a pokemon can't get a status condition normally, like Steel Pokemon can't be poisoned, Synchronize still follows that rule.