1. Black Bat was an Amalgam Comics character, a fusion of Batgirl and the Black Cat:
2. Black Bat was a pulp hero who came out around the same time as Batman and there were lawsuits back and forth where each party accused the other of a ripoff. From wikipedia:
Both the Black Bat and Batman hit the newsstands around the same time, and both claimed that the other was a copy. The threat of lawsuits ended when DC editor Whitney Ellsworth intervened. Ellsworth had once worked for the Black Bat's publishers and brokered a deal that allowed both characters to co-exist peacefully. It is probable that the costumes of both characters were copied from the 1933/34 Black Bat series which featured costumed illustrations of the Black Bat inside the pulps though actually the "Black Bat" in the stories was indistinguishable from any other man in his choice of clothing. Batman creator Bob Kane always contended that the only bat-like man he had seen was the villain from the 1930 film, The Bat Whispers. However, the Black Bat did have a permanent influence on the Batman: chief Batman scribe Bill Finger called Kane's attention to the unique gauntlets the rival character wore. Subsequently, similar "fins" were added to Batman's gloves which remain to this day.[source]
I'm going to go out on a limb and say that Morrison wasn't going out of his way to reference the Black Cat, so I'll discount that example.
As for the pulp character of the Black Bat, I'm not sure if DC was referencing him or not. Would this "Black Bat" be public domain at this point? I assume there are at least not active trademarks on the name, or there wouldn't be the Amalgam character. Would there even be a problem if it's spelled "Blackbat" instead of "Black Bat?"
It's interesting because the character of Black Bat is—I've learned from flipping through the summaries—a gun-toting crime-fighter who pretends to be blind during the day so he can do superheroics at night. That sounds like Batman, Daredevil, and Punisher all rolled into one. However, it sounds nothing like our Cassandra Cain. I hesitate to assume either of these characters are being referenced because 1) neither are anything like Cassandra and 2) neither are DC characters (or at least, only DC characters).
Anyone know more about these characters? Anyone know of some other character they might be referencing with 'Blackbat'?
(Note: For some general discussion about the name, see Woerlan's thread here.)