So, not sure exactly how NICS works if it is a database that includes the names of prohibited individuals or a program that links to other databases that contains these names.
Either way it would seem if anything was unconstitutional it would be the process that adds your name to the database not the actual database itself.
A major source of objection to a free economy is precisely that it ... gives people what they want instead of what a particular group thinks they ought to want. Underlying most arguments against the free market is a lack of belief in freedom itself.
- Milton Friedman