Michelle Alexander, in The New Jim Crow, suggests that if all defendants declined plea agreements and opted for trial, the criminal justice system would grind to a halt under the weight of all those trials. Prosecutors would be overwhelmed by the work needed to prove their cases beyond reasonable doubt.
Imagine what would happen if all sex offenders refused to register.
One after another, offenders would be charged with failure to register and packed off to prisons that are already overcrowded. That's the part of the scenario that would be hard to live with. On the other hand, since the registry makes it difficult for sex offenders to find employment, many of them do have time on their hands.
A few years of conscientous objectors, courts wheezing under the load of FTR cases, voters being hit with the expense of building new prisons...maybe this would deal the fatal blow to the registry.
The part I can guarantee is that the incidence of sex offenses would not increase.