That would rather depend on why that person had blue eyes. If the basis of his blue eyes was genetic then a classical genetic analysis like Kuresu has done will tell you the likelihood of the
gene being passed on and whether or not the trait was expressed in the progeny would depend on the nature of the trait, i.e. if it was reccessive/dominant etc....
If the basis was not genetic, i.e. environmental or epigenetic, then the trait might very well be lost from the progeny, although there are a number of examples of epigenetic inheritance of traits, such as in agouti mice(
Morgan et al., 1999).
TTFN,
WK