No, they will make a permanent registry -- catalog guns of those to submit -- then viciously prosecute those found not to have submitted.
Records exist going back decades as to who owns what guns.
Many people will fall in line to protect themselves and their families.
I might well submit, for that reason, as I make 4 times as much as my wife, and she and my 3 kids need that money to survive -- particularly in these times.
Guns will be widely available, just more expensive. Argentina is a recent example of where we're headed.