I cant gauge the depth of the cut from the picture, and i dont know how deep mine was. But I've been driving on a tire with a similar cut (only a little longer) for almost 7k miles now. (that is, until the other day, when i made my car no longer driveable...)
Lemme see if i can find a pic. Nope, cant find one, not even on my back-up disk
I would take it to a tire place and have them look at it.
But...i think it would be ok (I am in no way responsible for anything that happens...)