Ofcourse. "kart melli" is needed for passport renewal, letter of power of attorney and such. Why do you want to leave it in Iran? As far as I know, it worths wherever you are. I don't think that anybody can sell or buy a house for you with your "kart melli" (or can he?). I brought all my original documents (even my marriage certificate) to Canada. Believe it or not, 4-5 years ago, I had to show an original copy of my marriage certificate to my employer!
Now that the Iranian embassy is going to be closed, I still think that you have to have all your own documents in hand.