The two concepts have historically been inexorably linked in sci-fi, which will likely make the first AGI harder to recognize as AGI if it lacks consciousness, but I'd argue that simple "unconscious AGI" would be the superior technology for current and foreseeable needs. Unconscious AGI can be employed purely as a tool for massive collective human wealth generation; conscious AGI couldn't be used that way without opening a massive ethical can of worms, and on top of that its existence would represent an inherent existential threat.
Conscious AGI could one day be worthwhile as something we give birth to for its own sake, as a spiritual child of humanity that we send off to colonize distant or environmentally hostile planets in our stead, but isn't something I think we'd be prepared to deal with properly in a pre-post-scarcity society.
It isn't inconceivable that current generative AI capabilities might eventually evolve to such a level that they meet a practical bar to be considered unconscious AGI, even if they aren't there yet. For all the flak this tech catches, it's easy to forget that capabilities which we currently consider mundane were science fiction only 2.5 years ago (as far as most of the population was concerned). Maybe SOTA LLMs fit some reasonable definition of "emerging AGI", or maybe they don't, but we've already shifted the goalposts in one direction given how quickly the Turing test became obsolete.
Personally, I think current genAI is probably a fair distance further from meeting a useful definition of AGI than those with a vested interest in it would admit, but also much closer than those with pessimistic views of the consequences of true AGI tech want to believe.