On the Mine map, posession of the War Idol by either player does not appear to make any difference to the numbers of the spawning waves. The spawns of both sides are always identical, no matter who owns the Idol. (over many waves too, so its not just a wave spawning before the Idol is taken)
Map spawn settings:
Spawn rate: Normal
Grunt Strength: High
War Rank Speed: Normal
War Rank Start Level: 1
You know, I didn't believe you for a second. I figured someone would have caught this, so I decided to test it as scientifically as I could. I started a game with adjustable game speed enabled, no ai, and put me on the good team. I then captured the flag, ran to the back of my base, and set the game to +10. I then grabbed observer totem and the teleport and watched as wave after wave had the same number and composition of troops. So, I thought, "well they must be stronger." I resterarted did the same thing, but this time sat in the base and didn't leave.
Trial 1: My troops reached citadel at 36 minutes.
Trial 2: My troops reached citadel at 34 minutes.
Now mind you they reached the citadel by killing all defenses, but could not take it out. The citadel would regen all health before reinforcements could arrive. Seemed conclusive, but I figured I would try 1 last time.
Trial 3: My troops reached citadel at 1hour 35 minutes.
Trial 4: My troops reached citadel at 1 hour 22 minutes.
Trial 5: Niether sides' troops reached the opposing citadel in 2 hours.
I am truly confused, but it would seem you are probably right. It seems like the war idol flag does not currently work, or at least it does not work well.