I would imagine if you did it excessively to the point of breaking the skin and then continue to do so you could risk a sort of infection caused by something in the ink itself, but other than that there is nothing medically dangerous about writing on your hand. The ink does absorb through the pores of your skin but it doesn’t reach your bloodstream, and even if it did, it wouldn’t matter.
Tattoo artists break the skin everyday and, with the exception of dirty needles, do not harm their clients.
So, yes.