You do take more damage while cloaked, in the sense that your shields are down. This is why it's usually suicide to cloak while under fire, unless you've got polarize hull, Brace for Impact and maybe 1 other good hull buff in place to keep you from getting eviscerated. The only other exception is when the attacking feddie is so inept that his weapons barely do damage.
Are you talking about Battle Cloak or regular cloak?
Ships under regular cloak do not take direct hull damage. As soon as it goes to Red Alert, the shields are up instantly. Which means, it's ups before the weapon fire even comes close to the hull.