Yes, this is one possibility. If the black holes were originally normal matter which formed after this era, then this baryonic component would have been involved in nucleosynthesis and would thereby have affected the cosmic abundances of helium, deuterium and lithium relative to hydrogen. At the present time, these abundances are consistent with a limit for baryonic matter of about a few percent of the critical density ( Omega). This is not enough to account for the amount of dark matter at cosmological scales. And as for galactic scales, factors from 2 - 5 times the luminous matter seem required. It is possible that some fraction of this galactic dark matter could be in black holes, neutron stars and sub-luminous matter which formed after the Nucleosynthesis Era.
If you form black holes before the Nucleosynthesis Era, then the element abundances are only constrained by the baryonic component that escaped being a part of these 'primordial' black holes. In principle, you could hide all of the dark matter in such primordial black holes, and still have the element abundances yield the result that the baryonic matter is only a few percent of the critical density. This would be an interesting solution to this dark matter mystery, but you would have to prove that dark matter is, in fact, in the form of optically silent black holes, and that these do in fact date from BEFORE the era of nucleosynthesis. This is not easy!