No, thank you.
1) Criminals will never sign up, so the only ones bearing the cost will be those who want to legally own guns.
2) Having the equivalent of an entrance exam to exercise a fundamental, individual right is a monumentally bad idea. Why not just have a civics exam before one can vote, and a grammar test before one is allowed to write letters to their Congressfolks?
3) Costs = astronomical.
4) Potential for abuse = gigantic.
5) Amount of anticipated federal meddling = gargantuan.
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.