Does any parser ever parse non deterministic unambiguous context free grammar?
There are a number of general parsing algorithms (Earley, GLR, GLL, etc.) which can handle arbitrary context free grammars, even ambiguous grammars. (For ambiguous grammars, an entire parse forest is produced, usually as a spaghetti-like graph structure, because grammars can produce an infinite number of parses, or an exponential number if null cycles are removed.)

What these parsers cannot do is parse any grammar in time linear to the length of the input. It could take up to cubic time, although GLR parsers can parse unambiguous grammars in quadratic time even if the grammar is non-deterministic. (In practice, GLR parsers tend to be close to linear time for typical applications, because the grammars are "mostly" deterministic and unambiguous.)