Disconnecting the ground is a bad idea, having it grounded to a solid frame point is a very good idea. All mast antennas will act as a ground but that's not their intended purpose. The reason for that is that they rely on their shield being grounded to help reject noise. Asking the antenna to carry the ground current from the radio isn't a good idea, as it can slightly reduce your radio reception (especially if you listen to AM) and it just not the best ground. Inside the head unit all of the grounds (antenna, RCA, amp, etc..) are connected together so grounding any of them will ground all of them. But depending on the design of the unit you might be asking a tiny little sliver of board trace to carry all of your ground current, which is bad idea. Nissan's did not use the antenna as the main ground, they used the radio's metal chassis which was bolted to the metal frame of the car.
That being said, using a multimeter check the yellow and red wires for voltage while grounding the meter to the same ground point as the radio. Or ground it to the outer chassis of the radio. A test light will tell you something is there, but you need to know that you are getting +12v. A test light can't tell you the difference between 9.2 and 11.1, so it's important to use a meter.