If you're playing on normal mode then no, don't restart. All the black card will net you is the SP12 which you can replace with the AS12 when the time comes (and there isn't much you need to kill with the SP12 before the AS12 becomes buyable). That being said you will still have to buy buckshot for a time but you should be using the M4A1 + Hammer at this point so the other ammo boxes wouldn't really help you.
"Attack while it's tail's up!" -God bless FF7 and its grammar.