Whether plant variegation can be passed through seed depends on what is causing the variegation. “Variegated” describes a visible phenotype, not a single genetic mechanism.
Genetic variegation
If a variegated phenotype is caused by a heritable nuclear genetic variant, it may be transmitted through sexual reproduction. The proportion of seedlings showing the trait depends on the inheritance pattern and the genotypes of the parents.
Chimeric variegation
Many prized vegetatively propagated variegated plants are chimeras, meaning genetically different cell populations coexist within the same plant. Sexual reproduction does not simply copy the layered cellular arrangement of a chimeric shoot, so seed from a visibly variegated plant should not automatically be expected to reproduce the parent's pattern.
Why can a variegated parent produce green seedlings?
The reproductive cells that form seed originate from particular cell lineages. The cells responsible for visible variegation elsewhere in the parent may not contribute the same variant to the gametes. Recombination and segregation also make seedlings genetically different from the parent.
Plastid inheritance
Some variegation involves chloroplast or other plastid genomes. Plastid inheritance differs among plant groups and can be strongly maternal, paternal or biparental depending on the species, so the outcome cannot be generalised from leaf colour alone.
What about a random variegated seedling?
A variegated individual appearing in an otherwise green seed batch can result from a new genetic event, plastid variation, developmental mosaicism or other causes. The phenotype must be observed over subsequent growth before its stability or inheritance can be inferred.
Seed propagation versus cloning
If preservation of a particular vegetative phenotype is the goal, clonal propagation from appropriate plant tissue is usually more predictable than seed. Even then, variegation stability depends on the underlying biology and the tissue used for propagation.
Read more in how plant variegation works and our guide to propagating variegated aroids.