I don’t know if its an allied advantage–plenty of times the described endgame comes and the Axis clear Moscow with 6 or so units left, then they only have to survive one round of Zombies attacks, they win. In an equal number of playouts, the zombies eat the remaining Germans so the Germans would have to rush Moscow again (along with Japan throwing its airforce at it) and see if they can survive another round, plus another bite.
If they can, they win. If they cannot, allies would eventually win, though the game is going to go on for a while and is more up in the air than the first described scenario.
One thing I will say is that the addition of both tech and zombies are tedious and arbitrary–they extend certain parts of the rolling game and add some new considerations to the old system that require more planning, and thinking–not to win, but just to accurately account for all those zombies, coming and going, and two types of hits, that can target two different types of units (but not incoming, yet to be allocated zombies).
In the normal game once the number of hits required has been rolled you can just say “wiped” and they can stop rolling and there is nothing else to do except retal (often rolled simultaneously) and clean up. In AAZ, you have to keep separate count of zombie hits rolled, excess hits rolled, and “zombies present vs zombies to be produced”. Yuck.