I think the CCW can get you exempt from NICs if your state meets the BATFE's requirements, which I think means running a fresh background check on all CCWers every year, among other things.
If the state agrees to that, your CCW can be used in place of the NICs check. If it doesn't, it can't. I think part of Wyoming's suit against the BATF was in part related to this. Wyoming had it's rules of restoring a person's 2A rights that the BATFE did not agree with. The BATFE came back and said that dealers in Wyoming could not used a Wyoming CCW to replace NICS.
http://www.jacksonholestartrib.com/.../wyoming/87c81c7070cde361872571e20082d4fa.txt
If the state agrees to that, your CCW can be used in place of the NICs check. If it doesn't, it can't. I think part of Wyoming's suit against the BATF was in part related to this. Wyoming had it's rules of restoring a person's 2A rights that the BATFE did not agree with. The BATFE came back and said that dealers in Wyoming could not used a Wyoming CCW to replace NICS.
http://www.jacksonholestartrib.com/.../wyoming/87c81c7070cde361872571e20082d4fa.txt