The only significant 2nd Amendment case argued before the Supreme Court in decades was the
Heller (aka Parker) case. I don't believe the NRA was involved in any proceedings in the
Heller case, nor did the NRA provide financial support.
In fact the NRA opposed bringing the Heller case to court at all.
Cato Institute senior fellow Robert Levy, co-counsel to the Parker plaintiffs, has stated that the Parker plaintiffs "faced repeated attempts by the NRA to derail the litigation."
The challenge to D.C. law was initiated by Robert Levy who financed the
Heller side.
Alan Gura, of the D.C.-based law firm Gura & Possessky, was lead counsel for Heller, and argued on his behalf before the Supreme Court.[40] Robert Levy, a senior fellow at the Cato Institute, and Clark Neily, a senior attorney at the Institute for Justice, were his co-counsel.[41][42]
The Supreme Court found in
Heller that the 2nd amendment provides for an individual right to keep and bear arms. Had it been up to the NRA, the
Heller case would never have been heard and that right would still be in doubt.
So the answer to your question is no. The NRA did nothing in the Heller case, and to the best of my knowledge has never brought or participated in a 2nd Amendment case before the Supreme Court.
However they will take your money and pay Wayne La Pierre $1,281,365 last year.
http://www.charitywatch.org/hottopics/Top25.html
http://en.wikipedia.org/wiki/District_of_Columbia_v._Heller#National_Rifle_Association