Is there any relation between the Bynar and the Borg?
No, the Borg are not connected to the Bynar. They do share some superficial similarities, but the Borg's technological superiority is based on nanotechnology whereas the Bynars rely on much cruder surgical enhancements.
MONINGER: I believe you're looking at a form of nanotechnology. I found thousands of these in both aliens. They're not just regenerating the damaged tissue, they're repairing the mechanical components as well. As far as I can tell, this arm's as good as new.
DRAKE: The Denobulans have experimented with nanotechnology, but they have nothing like this.
Dr Phlox, when investigating the Borg comments on the fact that they're not the only civilisation to use tech to improve their biological forms.
PHLOX: There's a species I once encountered in the Beta Magellan system, the Bynars. When they're born, a surgeon removes the child's parietal lobe and replaces it with a synaptic processor. I saw the procedure performed once. It was very impressive.