The plot thickens...

I'm going to use furniture bolts so I was planning to counter bore the holes. I imagined I would have to do that in another pass but it might be possible to do it in a single pass with a bit like this:

Wealden Tool Company Limited Drill Counterbore

If I can find one big enough (10mm pilot, 16mm counter bore, 25+mm cutting length)... is that likely? I would have to counter bore on each face anyway so that would remove the advantage of through drilling if I could drill and counter bore at the same time.