No. They should remain on the cooldown, because going from Sword to Shield Oath gives you 20% damage reduction instantly. When you turn on Shield Oath you instantly gain the benefit of being tankier. Grit, which also does this, also costs a GCD to use, not to mention almost 4 times the mana. Defiance, the only tank stance that is off global and doesn't cost mana has the downside of NOT making you tankier as soon as it is applied, you need to be healed for it to have any effect. It increases your max HP, not your current and also increases healing received, which again requires healing to have any effect. Meanwhile, you lose the 5% extra damage (and up to 10% crit chance) from Deliverance, and immediately lose a further 25% damage from being in Defiance.

War stances also have the downside of having a long recast. If you change stance you're stuck with it for a while. PLD/DRK can swap as often as they like, mana permitting.