No, it would be unconstitutional to quarantine all gun owners. As everybody knows. Are you actually an NRA troll, that you ask a deliberately foolish question like this?
Every time that someone raises an idea like this, it ignites a huge rightwing backlash against "liberals" by fearful gun owners, and generally weapons sales increase, because many gun owners fear a general confiscation of all their firearms and rush out to buy more as insurance against the Evil Day.
As an article in Esquire pointed out a year or so ago, the firearms industry therefore loves talk about quarantining all gun owners or confiscating all guns. They boost sales, at a time when the gun industry might otherwise face a glutted market because so many gun owners already own so many weapons. It's important to scare people with the specter of total gun confiscation, Obama dictatorship, attacks by black painted UN helicopters in the pay of the Illuminati, etc etc. to get people to buy more.
The US pattern of private handgun ownership is obviously pretty stupid. It contributes to drug gang violence, random shootings in low-income minority neighborhoods, and the occasional murderous idiocy of a Newtown school shooting, the Batman murders in Aurora Colorado, additional Columbine murders, etc. etc.
But the way US politics goes at the moment, there's not much to be done about this. The forces for gun control can't win. It would be smarter for them to give up trying, so they don't provide new political "ammunition" for the gun manufacturers and the NRA.