Such genome transplantation was performed between two Mycoplasma species in Craig Venter institute Genome transplantation in bacteria: changing one species to another. They found that the donor genome completely changes the recipient cell to accept the identity of the original donor cell.
Note of caution: the above experiment was conducted between two highly similar species, and as of yet it is unclear what is going to happen if the exchange is performed between two distantly related bacteria species.
As for eukaryotes -- the transplants may be not viable at all, because naked DNA is going to lack epigenetic information (histone modifications, DNA methylation) that is preset during gametogenesis.