The current should not have an effect. However, it is possible that a dimer may dissociate. You could try treating your sample ± a cross-linking agent before resolving on native PAGE
Reasons for 2 bands in native PAGE can be protein isomers and post-translational modifications (phosphorylations, methylations. I don't think you can separate protein subunits by native page.
I have never heard of electric current in a gel having an influence on the association of protein subunits in native PAGE. However, sieving by the gel during electrophoresis might have an effect if the dissociation constant of the subunits is in the same range as the protein concentration so that the sample has the potential to be a mixture of associated and dissociated subunits. As they pass through the gel and become diluted, some dissociation would occur, leading to smearing of the bands or multiple bands.