Correct, that should be one of the challenges against it, plenty of 1st Amend case law to use, from both voting and anti-abortion cases.
That is the one thing I don't understand about the gun lobby, since '08 the 2nd has been deemed an individual right, the expression of such is a 1st Amend., all ant-gun legislation should be challenged on 1st Amend grounds, if they do, they should all fall. All that has to be done, is replace "gun" w/abortion or voting, and the laws should be found as unconstitutional.