The meaning of cum is combined with; also used as (used to describe things with a dual nature or function).
For example a sofa cum bed
Can it be used with humans as well like
My friend cum brother?
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As you might expect, the formal Latin cum (meaning with) is particularly used in academic contexts - such as [to graduate] cum laude = with honour(s).
There's an orthographic quirk whereby to come [to a sexual climax] has led to the unusual noun spelling cum = ejaculate (though the verb form is usually still written as I'm coming!, Did you come?, not I'm cumming!, Did you cum?). So it's possible some "non-academically-inclined" readers might primarily associate the quirky spelling with sexual overtones, not the Latin origin. But one shouldn't pay too much attention to such "snigger potential" (it would often be considered "childish" to even acknowledge it, let alone laugh oneself).
My personal choice would be to write about my friend-come-brother. Which I interpret as a "reduced" form of, say, my friend who can become my brother [in appropriate circumstances].
This distinction only applies in speech, obviously. And I'd hazard a guess that the majority of native Anglophones might not even realise that the majority of published writers use the cum spelling in this construction (because they don't know that spelling at all; most natives Anglophones aren't as knowledgeable about orthography, academia, and Latin roots as most published writers/editors).
As regards OP's specific question (can this construction be used of people?), the answer is it's a complete non-issue. Of course you can.
In American English, "brother" is often used as a synonym for "male friend." If it is intended to make clear that a male is a very close friend but not technically a brother by blood or adoption, a phrase similar to "my friend, who is as close to me as a brother" would be used.
The use of "cum," pronounced "coom," is rare in American English and virtually absent outside academic or quasi-academic discourse. The use of "cum," pronounced like the verb "come," in the sense that you are describing is simply not heard in American speech. For example, the common American term is "sofa-bed," not "sofa cum bed" or "sofa come bed."
I see no reason why "cum" can't be used for humans, to indicate two separate roles combined in one person:
I have a chauffeur cum gardener in my employ.
Aside: many place names in the UK use it to indicate two parishes combined as one, such as Shingay-cum-Wendy and it is not always hyphenated. It has the same usage as in the question.
Similarly please see the usage in Oxford Dictionaries for "study-cum-bedroom."