First, before NICS could be challenged in any real sense, the federal laws that have made certain persons, prohibited from receiving and possessing firearms, would have to be overturned. That is not at all likely.
See generally 18 USC § 922(b), (d), and (g): http://www.law.cornell.edu/uscode/text/18/922
Then there are the various State laws that do the same. Striking the federal laws would not do away with any corresponding State laws. Those too would have to be challenged and overturned. Again, not likely.
decision advises us that these restrictions would most likely be constitutional. Therefore...
The NICS check is a narrowly tailored regulation that serves a compelling governmental interest. It does not infringe upon the right to buy a firearm. It merely checks to see that you are not a prohibited person, before allowing the transfer to proceed.
It is my opinion that the NICS law will stand up to strict scrutiny.