Can knowledge of suchness or emptiness be achieved through cessation of conceptualization? Inspired by this comment and this answer I wonder, can the first bhumi be gained via the complete cessation of conceptualization? ie, if one achieves the complete cessation of all concepts is this equivalent to the direct realization of emptiness? If so, then what of someone who arises from meditation and continues to have no conceptions... is this a Buddha? 

Is the complete cessation of conceptualization equivalent to complete and perfect enlightenment? If not, then what has been achieved with the complete cessation of conceptualization? Anything?

It is my understanding that at least Je Tsongkhapa does not agree that this is equivalent to realizing suchness. From the Lamrim Chenmo Volume 3 page 16:


  It is said that the Chinese master Ha-shang (Hva-shang), having seen
  this sutra’s very clear and undeniable explanation that insight is
  discerning wisdom, exclaimed, “I don’t know how this can be a sutra!”
  and kicked it. He did this because the sutra’s statement did not agree
  with his claim that since all conceptualization of any sort involves
  an apprehension of signs, you should dispense with discerning wisdom
  and meditate on the profound meaning by not bringing anything to mind.
  This approach has a great number of adherents.


There are many other places where Je Tsongkhapa points out sutras that seemingly do not agree that the complete cessation of conceptualization is the same thing as discerning wisdom or the direct realization of emptiness which is said to unlock the first bhumi.

In my understanding, the direct realization of emptiness is a mental direct perception that does not involve conception. Perception is defined in contrast to conception where the latter is elaboration, proliferation of an object that generally takes place subsequent to perception. Still, it is said in my tradition that even with the complete cessation of conception and engaging only in direct perceptions that the appearance of inherently existing objects persists in sentient beings. It is said that other than a Buddha, only in an Arya being's meditative equipoise on emptiness does the non-perception of inherent existence occur.

Is this a matter of disagreement within modern traditions of Tibetan Buddhism? What are the other viewpoints?
"Thought" is a rather vague concept. When two people say "cessation of conceptualization" they could mean two completely (or partially) different things.

When I wrote that comment and that answer, I did not mean that one has to stop all thinking. My teachers and my books all agree that complete suppression of thinking is not the target state nor the path to the target state. One Lama said: "we're not training to be a rock or a donkey".

Instead, cessation of reification is more like going from "discrete" thinking to "analogue" thinking. Meaning, you no longer have a notion of particulars, everything becomes fluid and somewhat ambiguous but also multidimensional and "quantum". As Dogen said: "Enlightenment is ambiguity".

Something like this (in different words) is described in e.g. "Mahamudra: The Moonlight" by Dakpo Tashi Namgyal (Chapter 3).