Yeah, she'd insist she's Batman, but admit she's not the one he knows if he pressed her on it. Which would be obvious, probably, what with the full face cowl and voice modulator and being like half Bruceman's size.

It wouldn't be hard to figure out it's Batgirl in a new suit?? I feel like she'd probably tacitly admit that much to him, at least to try to set him at ease