No, it's not a sound argument, and is representative of a minority. You can expect emotions to run rampant for some people after a mass shooting.
That is a very common counter argument. I would guess that any new gun laws consistent with the second amendment will not eliminate mass shootings. So, arguments that this or that law will not solve the problem is avoiding the problem.
What I think should happen is that gun buyers should licensed like cars. You can't buy a new or used car from a dealer or private transaction without filing registration papers with the government. There is a readily available database of cars and owners so that stolen vehicles can be traced. Just like cars, the laws can't be enforced unless someone is caught without a license. In that case further penalties are in play. As I understand it, there is no computer database for guns; only a very incomplete and awkward paper trail to trace gun ownership. With cars, it is easy to trace interstate ownership.
Of course licensing and registration will not eliminate murder or mass shootings, but it will make it easier to apply further penalties for use of guns in felonies, and cause certain people to think twice about amassing weapons.