Unlocking a broken-screen nexus 6
You said in your post that you want to unlock it, so you can do a data wipe / factory reset on it? Right?

Why don't you just take a hammer to it?

Maybe toss it into a fire?

To answer your question... No. There is no way to enter the pin on that phone if you cannot use the touch screen. The only thing you would be able to do to that phone now is do the "hard master reset" by pressing the button combination for that phone. That would also delete all the data stored on that phone.

To find the master reset button combination for that phone, try using Google or going to xda-developers.