syntactic analysis - Can a noun be an adverb?

This question, which I first posed on the ELL site a few weeks ago, remains effectively unanswered. Although there an answer did finally get
posted, it seemed to be more of a parody of an answer than a real one,
to me at least.

So here goes; please consider this sentence:

I can barely see a foot in front of me in this fog.

As a standalone sentence, it can’t be the answer to a question starting
with “What can you...” because “a foot” is here a unit of the length of
vision, and so a question it may be the answer to might be “How far can
you see in this fog?"

Would I be right saying that *barely° in this sentence modifies can

whereas a foot modifies to see? If so, does it mean that it plays the
role of an adverb? But can a noun be an adverb? If so, what type of adverb
is it in that sentence?

P.S. There’s a related post on the ELL site dealing with the role of a
foot in a sentence, but it doesn’t seem to answer my question.

Answer

I can barely see a foot in front of me in this fog.

A foot here in English means a single foot, one foot. One foot is a distance. The determiner a is often used in lieu of one.

Barely is an adverb, other adverbs would work here:

I can almost see a foot in front of me in this fog. [substitutions]
I can hardly see a foot in front of me in this fog.

Almost, hardly and barely all qualify how the subject I in the sentence can see. Therefore, they are adverbs. These adverbs are often pre-positioned, unlike well which is often post-positioned.

To see a foot is a perception of distance. A measurement of distance. To perceive a distance. See is perceive (Merriam Webster).

Here is a scientific example of this usage:

Because both the incident fast neutrons and the emerging /spl gamma/s
penetrate fairly effectively, it ought to be possible to see some
distance into the ground.

Substitution for purposes of like structure: to see ten feet into the ground may be substituted in the text above. The seeing (perceiving) action is being performed by a detector.

The verb see means to perceive "with sight" and is transitive here. foot and distance are its complements in the preceding examples. [direct object complement of the verb see]

Ergo, foot is not an adverb or adverbial. One is hard pressed, furthermore, to see it as adverbial given the presence of barely in front of the verb to see.

to see a foot=to perceive a distance of one foot

The OP's sentence is the same as:
I can barely perceive a distance of one foot in front of me in this fog.

Answer to question: No, the noun foot cannot be a adverb.

see some distance