Stream of consciousness is described as...
a narrative mode that seeks to portray an individual's point of view by giving the written equivalent of the character's thought processes, either in a loose interior monologue, or in connection to his or her actions.
There are a number of famous works written in with this format: Ulysses by James Joyce, and J. D. Salinger's The Catcher in the Rye, for example. However, I do not see Franz Kafka's story, The Metamorphosis as an example of "stream of consciousness."
While the reader is aware of Gregor's thoughts and feelings, there is not a sense of disjointed ideas that are strung together—like ideas without punctuation. We do not think with punctuation, which would confine our thought processes. There is no such thing as a complete or incomplete sentence when we ponder a question. However, the use of punctuation makes our writing and what we read much easier to follow, though it might be seen as "contrived" to the author trying to present an accurate facsimile of what transpires in one's mind when thinking.
However, in reading Kafka's tale of the young traveling salesman who changes overnight into a life-sized insect (often associated with a cockroach, though a specific kind of bug was not Kafka's intent), the reader can see that the thoughts of Gregor are delivered without thoughts streaming together.
“This getting up early,” he thought, “makes a man quite idiotic. A man must have his sleep. Other travelling salesmen live like harem women."
Gregor's thoughts are concise and carefully presented. While there is indeed monologue delivered by Gregor's character, there is nothing "loose" about it. Gregor's thoughts are conversational, but carefully separated and understood. Stream of consciousness is often difficult for the reader to follow, which is not the case in this tale. A straight "narrative" mode is used by Kafka to present the plot of the story.