In a word, no.

First, remember that there was a great variation of standards of living depending on income, and location. Solomon Northrup's father was a property owner and he was relatively well educated. He likely was much better off than the average Negro at the time. The movie depicted an idyllic scene, but few, if any, whites in the 1830's would consider any black man an "equal", certainly there were friendships, but legally there was no comparison.

Segregation was a step forward. Before "separate but equal" municipalities simply didn't offer those amenities for colored people.

Southern freemen had it even worse. Some slave codes applied to free blacks as well, in some states it was illegal teach even free blacks to read. Freemen had to carry their papers at all times, and any white man could force any black man to show their papers.

And, of course, there was always the specter of being kidnapped and sold into slavery just as Northrup was.

"Free negroes belong to a degraded caste of society; they are in no respect on an equality with a white man. According to their condition they ought by law to be compelled to demean themselves as inferiors, from whom submission and respect to the whites, in all their intercourse in society, is demanded; I have always thought and while on the circuit ruled that words of impertinence and insolence addressed by a free negro to a white man, would justify an assault and battery" -Wilson, Black Codes (1965), p. 27. Quoting John B. O'Neall, Court of Appeals of South Carolina, in State vs. Harden (1832).

If you are really interested, I would suggest reading The Black Codes of the South, by Theodore Wilson.