For "intelligence" in the abstract? No. But going back to the "human like" distinction... humans generally seem to have goals, so arguably an AGI that would register high on the "human like index" would have goals as well. But would an AGI necessarily have the same kinds of goals as a human? I can see plenty of cases where the answer would be "no".

Take hunger for example... humans often have a goal to "find food". An AGI running on a rack of servers in a data-center doesn't exactly have a perfect analogue for that. I guess you could set up some kind of metaphor based on maintaining a quality electrical feed, but those two things strike me as fairly different.

For instance, would its prime goal be to continue up leveling its intelligence?

My only contribution to that question at the moment would be to say that I think it might be over-simplifying to think in terms of the AGI having just one goal, or even having one clear "prime" goal. If there's no constraint that it be "human like" then I suppose its goal(s) can be whatever its designer programs in.

In the research I'm doing (which is very incipient and not particularly advanced at the moment) I'm exploring the idea of having the "AI" have a variety of internal metrics (I suppose you could consider them loosely analogous to human emotions) such as "boredom", "curiosity", "confusion", and so on. And the core processing loop may be driven by the "AI" trying to balance those various metrics. For example, if "boredom" is high, it may seek to engage someone in conversation, or go off and start reading Wikipedia pages.

If "confusion" is high it might start running internal simulations or using abductive inference to try and generate explanations for things it doesn't currently understand. Or if there is a current interlocutor engaged in conversation with it, maybe it starts asking "who, what, when, where, how, why" type questions.

A big hole in this scheme is that I don't currently know, or claim to know, exactly how to train it to use interrogatives to ask questions. I'm planning to start a deep dive into the current BOK on human childhood language acquisition to see if there is something to be borrowed from that world, but that's pure speculation on my part right now.