Can epigenetic structures carry a trait?
Yes, epigenetic changes does affect the phenotype. This is here the whole interest behind epigenetic. Environmental variation (incl. parental care) affect epigenetics which in turn affect the phenotype (incl. behaviour) of an individual. It is pretty much clear from the wikipedia definition of epigenetics


  Epigenetics studies stably heritable traits (or "phenotypes") that cannot be explained by changes in DNA sequence.


The term "phenotype" (or "phenotypic") is actually present 3 times is the first small paragraph of the wikipedia article.

For example, you can read here on wikipedia an example of a study showing that maternal care affect epigenetic variations which in turn affects stress level later in life as measured by HPA.