Hi Anastasia,
To answer your question: YES because it can be substituted, and it depends on the use of the word.
Articles ( indefinite “a”, “an” / definite“the”)
can be substituted depending on what you wanted to say.
With your first sentence:
“The people that I AM closest to, I met in the choir” (substitute)
or “The people that I AM closest to are the ones I met in the choir” (substitute)
Another use of this word:
ex:
“Jane is friendly, among my friends in the choir community, she is THE closest.
[OR] “Among my friends in the choir community, she is MY closest friend. (substitute)
In reference to: “I am closest to my mother”
there should be a context before or after this sentence.
If none, allow me to add a few notes...
You may say:
“I am close to my mother” (as we only have 1 mother and there’s no comparison, unless you wanted to state a situation where you were not close to someone but rather your mother then you wanted to say something like this:
[“I am closer to my mother, than my father”] as we only have 2 parents, so the use of "closer" is more appropriate in these sense.
or you wanted to emphasise ("emphasize") something
“Among my relatives I am closest to my mother” (a comparison to numerous people)
Have a great day!