If this occurred, it would have been among the black creole/cajun populations of Louisiana. I don't know for certain if they voted, but they definately married interracially (they had some old spanish legal tradition for designating the offspring of interracial couples) and they did allow blacks to serve various capacities in the militia dating back to at least the War of 1812. Tennessee also passed and enacted a law in June of 1861 to prepare for the defense of the state. One of its provisions was to recruit blacks as soldiers.
Never mind all the southern states that made it illegal for blacks to move in there
Wrong. Southern states typically had laws that placed either time restrictions or certain residency or property requirements on free blacks that wanted to live there. The northern states I spoke of previously, tu quoque boy, banned blacks from setting foot their outright. The census bears witness to this fact as the majority of free blacks lived in slave states.
were there any Northern laws that sold free blacks into slavery?
New Jersey, where emancipation effectively declared all slaves free but grandfathered some of them from enjoying that freedom, requiring that they continue in a servitude status if they didn't meet certain age requirements. Most of the Jersey slave owners simply sold their investments down south. A few kept their slaves until the civil war.
So to what do you attribute the growth in the black population of Illinois between 1820 and 1860? At a time when the free black population of southern states like Louisiana, Mississippi, and Arkansas was declining?