So, it’s true that if you complete the warchest on one account, while it doesn’t SHOW the progress of the warchest on another account you do still get the skins, you DON’T however, get the free row of unlocks. (I might have to double check the skins, but you certainly don’t get the portraits).
For example, if you complete warchest on one account, you will not have things like the classic banners and other unlocks that are part of the free row of unlocks (only the purchasable rows, assigned to the 3 races). Even watching twitch seems to not help this one to unlock, either. As twitch shows you to have completed the warchest.