Possible, yes but probable, no. (I assume that the history of the parental family as you mention is important)
Let us first consider HERC2 (H=brown, h=blue) and OCA2 (O=brown, o=blue) as per the names mentioned in the reference you cite, to be completely unlinked, such that they are independently assorted. Since the father's lineage has no history of the recessive phenotype(blue), and the genes segregate independently (our assumption), we can conclude that the father is homozygous for the dominant allele in both the genes(HHOO). In this scenario, it is very unlikely to get blue eyed children, but is still possible in the following two ways:-
The father's lineage does have a recessive gene (which probably entered his family gene pool due to non-consanguineous mates carrying a heterozygous phenotype in either of the gene pair HERC2 or OCA2), and has evaded expression by pure chance or because the recessive gene carrier entered into the family very close to the father,i.e. probably just one or two generations above the father(so that not enough generations have passed to allow the homozygous recessive trait to develop). In each of these cases, one or both the gene loci in the father might be heterozygous(HhOO or HHOo or HhOo) and coupled with the mother's heterozygous genotype(a good guess considering the history of many recessive phenotypes), might produce a blue-eyed child due to homozygosity in any one of the gene.
There is a mutation in the germinal cells of the father which creates a non-functional mutant allele and thus can give a blue-eyed child with a heterozygous mother.
But in either case, considering independent assortment, the chances are very bleak.
But if we also take into account the linkage of the two genes, then the probability rises significantly. Now there is a good chance that the father's lineage might contain a heterozygous (or homozygous recessive) allele pair on a single chromosome, which due to their tight linkage, might pass on without any recombinations and therefore might evade phenotypic expression more efficiently(although, since a dominant allele in both the genes is required for the dominant phenotype, the extra evasion efficiency due to linkage is less). As given at the end of your reference, suppose there is one chromosome in the parental ancestry that carries both the recessive genes. If they are linked, the chances of brown eyed parents to have blue eyed children decreases (and the chance of being heterozygous also decreases) thus making it more likely that the father's lineage could have a recessive allele in spite of there being no significant expression in his family history. Therefore, more tightly they are linked, greater is the probability that the father is heterozygous. Linkage does not significantly lessen the possibility for the father to have a blue-eyed child since the mother does contain a recessive linked- phenotypic pair in all probability. (Actually, the probability is also based on which combinations are linked, but the possibility of there being a heterozygous allele remains positive with most combinations).This again gives some chance for brown eyed parents with the history you mention, to have a blue eyed child.
In any case, there is a chance but the probabilities depend a lot on the linkage, the linked combinations, and the actual genotypes of the parents but there is always a possibility.
Just to add a bit of information, the kind of recessive epistasis we described here, where the homozygous recessive (at the hypostatic,HERC2, loci) phenotype resembles the phenotype for the recessive condition at the modifier pair (OAC1), is only a part of the story. Actually, certain polygenic influences further complicate the situation by introducing a variety of phenotypes. This is a good link to go deeper into the eye-colour genetics.