They're not related that I'm aware of, but it would be pretty cool if they were. However, everyone in the DCU named "Harper" is apparently related (Speedy/Arsenal/Red Arrow, Guardian, Tim's cop friend), so it wouldn't surprise me if any Drakes in the 'verse were related as well. But, wasn't that weather-controlling guy that Jaime defeated ("I have lasers and you have no pants. Do the math.") named Drake? They have a supervillain in their family tree. I am now worried for Dinah and Tim.
A while back, I had a thoughtbunny (related to, but different and often mistaken for, a plotbunny) of Tim "Robin" Drake being related to Bobby "Iceman" Drake of the X-Men, as well as Linda "Supergirl" Danvers being related to Carol "Ms. Marvel" Danvers.