Once you’ve had the natural chickenpox virus in your body the virus goes dormant in your nervous system until possibly one day when you’re under a time of extreme stress/immunocompromise and the virus reactivates. Reactivation of the varicella virus (chickenpox) causes shingles (zoster).
Since these kids have never had the chickenpox virus, theoretically they won’t get shingles later in life. That’s assuming the vaccine is effective, most everyone has been vaccinated, and these children do not get the wild virus.
We can’t expect that all children will be vaccinated, however, the chickenpox vaccine is so effective that the seroconversion rate (when antibodies develop to a detectable level in the blood) is around 95% in healthy children.(2) That means the vaccine works pretty well, so it should help create good herd immunity if most children are vaccinated, and thus, aid in the prevention of shingles for the uninfected/vaccinated later in life.
So, simplified–if you’ve had chickenpox you are able to get shingles. If you’ve never had chickenpox you are not able to get shingles. If you’ve had the vaccine, you’ve never had chickenpox so you shouldn’t get shingles.