I don't think I can give you a true answer to the actual question as posed, as I don't have a strict definition of "general intelligence". Nor do I have a solid definition of "critical" in context.
But... if we lean on our naive / intuitive understanding of what intelligence is and what it means to be critical, you might translate this as "would a general intelligence system need analogy-making in order to do certain things that it couldn't otherwise do?" Or to put it another way "are there useful behaviors that are enabled by analogical reasoning that can't be replicated any other way?"
In the strictest sense, I don't have an answer to either of those questions either, but there is at least evidence to suggest that the answer may be "yes". See, for reference, the Copycat paper by Hofstadter and Mitchell. From what I've seen, some of the kinds of problems Copycat solves are different from anything I've seen solved by other approaches. Now maybe it's just coincidence that nobody has tried solving those problems with, I dunno, let's say "deep learning" or "rule induction" or "genetic algorithms". Or maybe they have and I just haven't stumbled across that corpus of research.
Anyway, I'll also add that there is still ongoing research into using analogy for AI/ML. See for example this paper from July 2017 where the authors talk about using analogy, but define their approach as "analogical inference" (which they claim is different from "analogical reasoning" as defined during the earlier "GOFAI period"). There is also this paper from June 2017 where another set of authors deal with a form of analogical reasoning.
I don't think there's a consensus as to whether or not some form of analogical reasoning is "critical" but it's definitely a subject that is still being researched.
And to go off on a little bit of a tangent - an interesting related question would be to ask whether or not "analogy making" would be an emergent property of a sufficiently deep / wide ANN, or would such a facility need to be designed and coded up explicitly.