No, in No Man's Land Volume 5, they eventually got over the fact that Batman hadn't been there. Nightwing and Robin were there too, and upset that they were fighting. Nightwing said it felt like his parents were splitting up, since they had been sent upstairs so Gordon and Batman could talk. (Bruce revealed to Gordon that he was Batman, but Gordon refused to look, so he wouldn't have to know.)

I don't think Gordon knows Babs was Batgirl I. At least, he has never said anything for certain about it.

Batman let (he didn't know she was doing it.) Stephanie get her hands on some protocols that included taking over Gotham's underworld. A big gang war started, people were killed, cops were told to shoot anyone in costume on sight, and Stephanie was killed by Black Mask.

In the aftermath of everything, Batman was a wanted man.