That's a good point. If we don't figure out how to design for what we call consciousness it might be that what emerges from some future neural network is an alien mind that's very different from what humans would call conscious. Could that be called AGI?

That's still very distant from what people are calling AI today.

Nope, animals are conscious and yet not AGI, so the two aren't equivalent. Could consciousness emerge from any system capable of AGI? I doubt it: intelligence is only one axis, and consciousness probably depends on others, like memory, self-reflection (one's output feeding back as input), and continuous operation that reacts to events from both the environment and the self.