I have a question...

Possibly. We don't know much about dementors -- do they even have eyes? They thrive on misery, a feeling -- do they "find" people by sensing their feelings? Moody's magical eye could see through it. Is it possible that magic can be used to see through it? Was the story a literal "Death himself made the cloak" or was it a aesop fable, a metaphor, a similie, or just a story?

Also: did Dumbles know the cloak was a Hallow at the time? We know he suspected it, but did he know?

There's way to many unknown variables to be able to truly say.

yes but i really don't think that they can SEE you. i think they can sense your presence because i don't think they have eyes.They aint got no eyes. O.O

Dementors live off human happiness, they are such good guards of Azkaban because they can sense humans, they don't have to "see" them. Happiness to them is live bacon to men, a guy could find a plate of bacon with his eyes closed. Death wants to take the physical person(in the world of harry potter Death seems to be entirely physical), Dementors would take the soul, leaving the body. The invisiblity cloak only has to hide the physical body to protect them form Death.

Dementor can sense you they don't have eyes so invisibility won't save you.
And beside dementor didn't exactly kill people, they suck your soul and leave you in vegetatife state.

Maybe Dumbledore was not totally honest with Harry. I mean, he probably lied or at least spun a little yarn so that Harry may not go wandering too close to Dementors even under his cloak. These creatures are the least forgiving. The old wizard was so much manipulative that I would not be surprised by this.