Not necessarily.
My daughter has been exposed at least six times, by kids that had active eruptions (chicken pox parties) and has been vaccinated four times but still has no immunity to the chicken pox virus.
She may never get chicken pox but maybe when she is older who knows.
As a child I could not catch so much as the three day measles. Missed three days of school in twelve years.
When I was 27, my 1 year old daughter came down with chickenpox. She had maybe a dozen pox and never slowed down a bit. One week later I was down and out delirious with high fever and pox from head to toe. Forty years later she got shingles. One week later so did I. The gift that keeps on giving. When she was two, the mumps were going around. I grabbed her and we both went for mump shots. We didn’t get mumps.