"She needs a man."
Translation:Ona potrzebuje mężczyzny.
Normally, not. In written language I would rather reword it, but there is a possibility that someone might slip in spoken when trying to do an emphasis. This is not pretty (as this argument existing in the first place proves), but I can get the meaning just fine. I would still advise using your or mine proposition instead.
In my personal opinion : Ja, ty, my, Wy - cannot be used with "to" (in a meaning we are discussing)
but on, ona, ono, oni, one - not pretty but very possible in common speaking.
Also I don't like an idea of "caveman speaking" being applied to the way people speak - I am sorry that people who speak Polish mixed with Ukrainian or Russian because they stayed on the other side of border sound "caveman" to you.
While I agree it is stylistically 'not-cool', as far as I know there is no grammatical rule that would forbid such a construction. There are some examples of using 'równoważnik zdania' like that: "On to nie on.", "Ona to nie ptak." i "A ja to co? Pies?!" frequently shortened to "A ja to pies?!", so it is not like it truly doesn't exist in Polish – it is just rare, so it sounds odd/wrong. ;-)
If you know another Slavic language, then it might seem confusing to you, but Polish has separate words for a man (mężczyzna) and a husband (mąż). Similarly, there are also separate words for a woman (kobieta) and a wife (żona).
In contexts where you could replace "man" with someone, perhaps „człowiek” might be a better translation.
Just a little note: even Polish people sometimes make mistakes when writing Polish. There are many verbs that have the -ę ending in the first person and -e in the third, but some people write both with -e. So when dealing with casual writing, it's best to understand the context. The good thing is that the reverse doesn't happen.
W standardowej polszczyźnie niektóre czasowniki przyjmują dopełnienie w dopełniaczu zamiast bierniku. „Potrzebować” jest jednym z nich. Stąd „mężczyzny”, nie „mężczyznę”. Na co dzień zdarza się mi o tym zapominać i użyć biernika, ale w starannych wypowiedziach trzymam się dopełniacza.