I would not try it my self, it seems that it would be pretty dangerous covering them with the tattoo ink, it could cause an infection even. To be honest, I would talk to a dermatologist about options instead.
I think it also depends on the artist. I know people who have covered up scars with tattoos, but that kind of sounds like a lot of scars to cover. Unfortunately there will technically always be a scar there where your skin is indented no matter what pattern you put over it. Sorry =/
Hopefully this will help you I have a 3 inch scar on my arm I went to have a tattoo to cover it b ut they wouldnt they said it would bleed to much. Im sure it depends on how deep the scar is....Think before you just start covering your body in tattoos depending on what you do for a living you might still have to wear long sleeves