I've been checking the xml files and it seems you get no loyalty with the Sands for helping them during the war. This seems like a bit of an oversight. Effectively if they are disatisfied with you before the war you don't have much of a chance surviving afterwards as there is very few missions to allow you regain loyalty before they kill you.
IMO the whole way the mafia "war" could have been handled much better - and yes you are correct I believe. I'm pretty sure the same thing applies to Vargas if you decide to side with him in the war.
This shouldn't be a problem with respect to possibly getting executed, since although there are few missions available to regain loyalty, by the same token this means there are also few missions where you could lose loyalty (e.g. by not helping them or interfering when you shouldn't). And I'm pretty sure loyalty doesn't go down by itself when there are no missions from them.