This answer is in three parts:
Part 1 - Historical Denotations and Connotations of Smooch. A grounding in the meaning and usage of the word smooch in that time period is necessary to discuss the concept further.
Part 2: Literary Interpretation of "The Smooch" This provides my answer to the question.
(Hint: Yes, "smooch" has a significant literary and metaphorical role!)
Part 3: Conclusion
Part 1 - Historical Denotations and Connotations of Smooch
A more fundamental question is, "What did smooch mean at the time of this writing?" The Yellow Wallpaper, which is indeed a complex and brilliant piece by any measure, was published in 1892. The word smooch, which now means "to kiss and cuddle" had a different meaning in the 19th century.
According to The Century dictionary and cyclopedia (1897), it's the same as "smutch":
smutch: a black spot; a black stain; a smudge.
From A Dictionary of the English Language: Designed for Use in Common Schools Abridged from Webster's International Dictionary (Noah Webster, 1892):
Smutch (amuch), v. t. [SMUTCHED (amficht); SMUTCHING.] To smudge ; to blacken with smoke or soot. — n. Stain ; dirty spot. [Written also smooch.]
And The Proceedings and Transactions of the Nova Scotian Institute of Science, (Session of 1894-1895, Volume IX) describes the common range of usage of smooch:
Smoochin, hair-oil, or pomade. A young man from abroad, com mencing as clerk in an establishment at one of the outposts, was puzzled by an order for a “pen'orth of smoochin.” The verb smooch is also used as equivalent to smutch, to blacken or defile. We may hear such expressions as, “ His clothes are smooched with soot,” or “ The paper is smooched with ink.” But it is also used to express the application of any substance as by smearing, without any reference to blackening. Thus one might say, “ Her hair was all smooched with oil.”
So within this 1892 short story, one can understand smooch as meaning a "smudge" with connotations of something defiled, stained or dirty. Also important for a modern interpretation, smooch did not have any connotation related to kissing or cuddling.
Part 2: Literary Interpretation of "The Smooch"
This masterful work was not just about a woman obsessed with a yellow wall. She had an identity crisis, and the concept of "smooch" is a theme that recurs exactly three times in an escalating pattern.
- Then she said that the paper stained everything it touched, that she had found yellow smooches on all my clothes and John's, and she wished we would be more careful!
In this first mention, she is still "supposedly sane" and sees the smooch as simply the standard/normal/sane meaning. But she is frustrated and lost in the male dominated world. And her feelings are clearly repressed.
- There is a very funny mark on this wall, low down, near the mopboard. A streak that runs round the room. It goes behind every piece of furniture, except the bed, a long, straight, even SMOOCH, as if it had been rubbed over and over.
I wonder how it was done and who did it, and what they did it for. Round and round and round—round and round and round—it makes me dizzy!
Here she has recognized the smooch as something more. It is everywhere! Everywhere except the bed, where she was told she needed to stay. The smooch defines her place in the world. She belong in the bed. Not to do any type of work, even such as writing, but to rest in the bed. And, of course, the bed limits her identity to her sexual function. And this definition has been "Rubbed over and over" by generations of male dominance/oppression.
"I wonder how it was done and who did it, and what they did it for." The protagonist sees a process, an intention, and a motive in the smooch, which is the "stain" on her identity as a woman.
"Round and round and round-round and round and round--it makes me dizzy" here the protagonist is not saying something mundane, like "a smudge went all the way around". The smooch is something more and this discovery is making her dizzy. She is also becoming more "insane". But that's because she's discovering "the truth" of the profound blight of oppression that she lives in. A truth like this is dizzying. Recall when Neo takes the red pill in The Matrix, and goes down the rabbit hole. And when he wakes up in the real world, how jarring it is to discover that one has been oppressed their entire life, didn't know it, and just woke up to the reality.
- But here I can creep smoothly on the floor, and my shoulder just fits in that long smooch around the wall, so I cannot lose my way.
At this point, she is "certifiably insane" and her comments to her husband, taken at a surface meaning, are crazy enough to make her husband faint. His fainting is presumably because she "talking crazy talk" but it's not just that: yes, she's "out of control", but more importantly, she's no longer under his control. He also lives in a world supported by the male dominated paradigm, and seeing his wife no-longer living in that paradigm is too much for his consciousness. And as an aside, we are given an insight into insanity-as-sanity because we can also understand how her words do make sense from her perspective.
In this third mention of "smooch" she has discovered her identity. She realizes that she is under the smooch as she says, "my shoulder just fits in that long smooch around the wall". This is metaphorically true since she had always been under the spell of the male dominated world view. But once recognized for what it is, the smooch guides her. Keeping it in sight, she is no longer lost as she proclaims, "so I cannot lose my way."
Part 3: Conclusion.
Did the author intend all of this? Not by her own commentary. (See Wikipedia.) But then again, such a commentary might have been met with severe repercussions at the time. This very story proof to the point: it's about female autonomy (or the lack thereof) and in particular, the negative attitude towards women taking an identity as a legitimate writer!
There may never be any definitive proof one way or the other, but I would be inclined to believe that incorporating the smooch like this, and with the character's changing attitudes and relationship with the smooch, that the smooch acted as an intentional metaphor of her awakening to "the smooch on her identity", which also led to her personal self-discovery.