No because the blood won't leave the penis due to the pressure of the cock ring and cutting into the penis to relieve the swelling is likely to result in greater permanent damage than waiting for the FD and their diamond saw.
I don't think so. The tissues (corporate cavernosa) that fill with blood during an rection are basically like a fine sponge, and with the ring preventing any blood flow back out of those tissues... Yeah, you gotta cut that ring.