In a nation state, sure equality of outcome is possible because the simple fact of the matter is that through the oppressive nature of such states, basically everybody is poor except those in power. Everybody lives equally in the same misery.
Equality of outcome is a myth, a pipe dream that gets smoked through a bong during college from professors who smoked the same bong ignoring reality. When ever the term equality gets used, or was used in the Declaration of Independence, the term didn't apply for equality of outcome, but equality in that all are born the same, Tabula Rasa, those born with physical or mental disabilities not withstanding. Yet, even in such cases as those born with physical or mental disability can often time rise above such matters and achieve. Furthermore, the concept of equality doesn't mean that everyone can be born into the same situation's as every other man, and to try to accomplish that task, well see the first paragraph once more.
Equality as a concept has actually one of the narrowest definitions possible, the only thing that can be ensured when it comes to equality is equality of opportunity and protecting this ability to have same opportunity. This then leads to the Individual Rights that are also in the Declaration of Independence and the entire basis for the Republic that eventually got formed later in the Constitution, that we no longer live in as well, was to protect the Individual Rights so that everybody could have equal opportunity. Perhaps I will write my own hub on this matter in the future.